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  • 1.
    Artal, Enrique
    et al.
    Univ Zaragoza, Spain.
    Costa, Antonio F.
    UNED, Spain.
    Izquierdo, Milagros
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
    Correction: Professor Maria Teresa Lozano and universal links (vol 87, pg 441, 1987)2018In: REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS, ISSN 1578-7303, Vol. 112, no 3, p. 621-621Article in journal (Other academic)
    Abstract [en]

    Unfortunatelly an erratum appears in the foreword of this volume.

    We claim that one of the authors of the article On universal groups and three-manifolds, Invent. Math. 87 (1987), no. 3, 441–456 is W. Witten. The correct name of this author is Wilbur Carrington Whitten. W. C. Whitten is not the father of the fields medallist E. Witten, as we claim there.

  • 2.
    Artal, Enrique
    et al.
    Univ Zaragoza, Spain.
    Costa, Antonio F.
    UNED, Spain.
    Izquierdo, Milagros
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
    Professor Maria Teresa Lozano and universal links2018In: REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS, ISSN 1578-7303, Vol. 112, no 3, p. 615-620Article in journal (Other academic)
    Abstract [en]

    María Teresa, Maite, Lozano is a great person and mathematician, in these pages we can only give a very small account of her results trying to resemble her personality. We will focus our attention only on a few of the facets of her work, mainly in collaboration with Mike Hilden and José María Montesinos because as Maite Lozano pointed out in an international conference in Umeå University in June 2017, where she was a plenary speaker:

    I am specially proud of been part of the team Hilden-Lozano-Montesinos (H-L-M), and of our mathematical achievements

  • 3.
    Artal, Enrique
    et al.
    Departamento de Matemáticas, IUMA, Universidad de Zaragoza, C. Pedro Cerbuna 12, 50009 Zaragoza, Spain.
    Costa, Antonio F.Departamento de Matemáticas Fundamentales, UNED, Paseo Senda del Rey 9, 28040 Madrid, Spain.Izquierdo, MilagrosLinköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
    Special Issue: Dedicated to María Teresa Lozano conmemorating her 70th Birthday2018Collection (editor) (Refereed)
  • 4.
    Bartolini, Gabriel
    et al.
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.
    Costa, Antonio F.
    Departamento Matematicas Fundamentales, UNED, Madrid, Spain.
    Izquierdo, Milagros
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.
    On automorphisms groups of cyclic p-gonal Riemann surfaces2013In: Journal of symbolic computation, ISSN 0747-7171, E-ISSN 1095-855X, Vol. 57, p. 61-69Article in journal (Refereed)
    Abstract [en]

    In this work we obtain the group of conformal and anticonformal automorphisms of real cyclic p-gonal Riemann surfaces, where p⩾3p⩾3 is a prime integer and the genus of the surfaces is at least (p−1)2+1(p−1)2+1. We use Fuchsian and NEC groups, and cohomology of finite groups.

  • 5.
    Bartolini, Gabriel
    et al.
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.
    Costa, Antonio F.
    Departamento de Matematicas Fundamentales, UNED, Madrid, Spain.
    Izquierdo, Milagros
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.
    On isolated strata of pentagonal Riemann surfaces in the branch locus of moduli spaces2012In: Contemporary Mathematics, ISSN 0271-4132, E-ISSN 1098-3627, Vol. 572, p. 19-24Article in journal (Refereed)
  • 6.
    Bartolini, Gabriel
    et al.
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.
    Costa, Antonio F.
    Departamento de Matematicas Fundamentales, UNED, Madrid, Spain.
    Izquierdo, Milagros
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.
    On isolated strata of p-gonal Riemann surfaces in the branch locus of moduli spaces2012In: Albanian Journal of Mathematics, ISSN 1930-1235, E-ISSN 1930-1235, Vol. 6, p. 11-19Article in journal (Refereed)
  • 7.
    Bartolini, Gabriel
    et al.
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.
    Costa, Antonio F.
    UNED, Spain .
    Izquierdo, Milagros
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.
    ON THE CONNECTIVITY OF BRANCH LOCI OF MODULI SPACES2013In: Annales Academiae Scientiarum Fennicae Mathematica, ISSN 1239-629X, E-ISSN 1798-2383, Vol. 38, no 1, p. 245-258Article in journal (Refereed)
    Abstract [en]

    The moduli space M-g of compact Riemann surfaces of genus g has orbifold structure and the set of singular points of the orbifold is the branch locus B-g. In this article we show that B-g is connected for genera three, four, thirteen, seventeen, nineteen and fiftynine, and disconnected for any other genus. In order to prove this we use Fuchsian groups, automorphisms of order 5 and 7 of Riemann surfaces, and calculations with GAP for some small genera.

  • 8.
    Bartolini, Gabriel
    et al.
    Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.
    Costa, Antonio F.
    Dept. Matemáticas, UNED, 28040 Madrid, Spain.
    Izquierdo, Milagros
    Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.
    On the Orbifold Structure of the Moduli Space of Riemann Surfaces of Genera Four and Five2014In: REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS, ISSN 1578-7303, Vol. 108, no 2, p. 769-793Article in journal (Refereed)
    Abstract [en]

    The moduli space Mg, of compact Riemann surfaces of genus g has orbifold structure since Mg is the quotient space of the Tiechmüller space by the action of the mapping class group. Using uniformization of Riemann surfaces by Fuchsian groups and the equisymmetric stratification of the branch locus of the moduli space we find the orbifold structure of the moduli spaces of Riemann surfaces of genera 4 and 5.

  • 9.
    Bartolini, Gabriel
    et al.
    Linköping University, Department of Mathematics. Linköping University, The Institute of Technology.
    Costa, Antonio F
    UNED, Madrid.
    Izquierdo, Milagros
    Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.
    Porto, Ana M
    UNED, Madrid.
    On the connectedness of the branch locus of the moduli space of Riemann surfaces2010In: REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS, ISSN 1578-7303, Vol. 104, no 1, p. 81-86Article in journal (Refereed)
    Abstract [en]

    The moduli space M-g of compact Riemann surfaces of genus g has the structure of an orbifold and the set of singular points of such orbifold is the branch locus B-g. In this article we present some results related with the topology of B-g. We study the connectedness of B-g for g andlt;= 8, the existence of isolated equisymmetric strata in the branch loci and finally we stablish the connectedness of the branch locus of the moduli space of Riemann surfaces considered as Klein surfaces. We just sketch the proof of some of the results; complete proofs will be published elsewhere.

  • 10.
    Bartolini, Gabriel
    et al.
    Linköping University, Department of Mathematics. Linköping University, The Institute of Technology.
    Izquierdo, Milagros
    Linköping University, Department of Mathematics. Linköping University, The Institute of Technology.
    On the connectedness of the branch locus of the moduli space of Riemann surfaces of low genus2012In: Proceedings of the American Mathematical Society, ISSN 0002-9939, E-ISSN 1088-6826, Vol. 140, no 1, p. 35-45Article in journal (Refereed)
    Abstract [en]

    Let be an integer and let , where denotes the moduli space of compact Riemann surfaces of genus . Using uniformization of Riemann surfaces by Fuchsian groups and the equisymmetric stratification of the branch locus of the moduli space, we prove that the subloci corresponding to Riemann surfaces with automorphism groups isomorphic to cyclic groups of order 2 and 3 belong to the same connected component. We also prove the connectedness of for and with the exception of the isolated points given by Kulkarni.

  • 11.
    Bujalance, Emilio
    et al.
    Departamento de Matematicas Fundamentales, UNED.
    Costa, Antonio F.
    Departamento de Matematicas Fundamentales, UNED.
    Izquierdo, Milagros
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
    On Riemann surfaces with 4g automorphisms2017In: Topology and its Applications, ISSN 0166-8641, E-ISSN 1879-3207, Vol. 218, no 1, article id 18Article in journal (Refereed)
    Abstract [en]

    We determine, for all genus g≥2g≥2 the Riemann surfaces of genus g with exactly 4g automorphisms. For g  ≠ 3,6,12,153,6,12,15 or 30, these surfaces form a real Riemann surface FgFg in the moduli space MgMg: the Riemann sphere with three punctures. We obtain the automorphism groups and extended automorphism groups of the surfaces in the family. Furthermore we determine the topological types of the real forms of real Riemann surfaces in FgFg. The set of real Riemann surfaces in FgFg consists of three intervals its closure in the Deligne–Mumford compactification of MgMg is a closed Jordan curve. We describe the nodal surfaces that are limits of real Riemann surfaces in Fg

    The full text will be freely available from 2018-12-23 11:26
  • 12. Costa, AF
    et al.
    Izquierdo, Milagros
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
    On real trigonal Riemann surfaces2006In: Mathematica Scandinavica, ISSN 0025-5521, E-ISSN 1903-1807, Vol. 98, no 1, p. 53-68Article in journal (Refereed)
    Abstract [en]

    A closed Riemann surface X which can be realized as a 3-sheeted covering of the Riemann sphere is called trigonal, and such a covering will be called a trigonal morphism. A trigonal Riemann surface X is called real trigonal if there is an anticonformal involution (symmetry) a of X commuting with the trigonal morphism. If the trigonal morphism is a cyclic regular covering the Riemann surface is called real cyclic trigonal. The species of the symmetry or is the number of connected components of the fixed point set Fix(sigma) and the orientability of the Klein surface X/(sigma). We characterize real trigonality by means of Fuchsian and NEC groups. Using this approach we obtain all possible species for the symmetry of real cyclic trigonal and real non-cyclic trigonal Riemann surfaces.

  • 13.
    Costa, AF
    et al.
    Univ Nacl Educ Distancia, Fac Ciencias, Dept Matemat Fundamentales, E-28040 Madrid, Spain Linkoping Univ, Inst Matemat, S-58183 Linkoping, Sweden.
    Izquierdo, Milagros
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
    On the connectedness of the locus of real Riemann surfaces2002In: Annales Academiae Scientiarum Fennicae Mathematica, ISSN 1239-629X, E-ISSN 1798-2383, Vol. 27, no 2, p. 341-356Article in journal (Refereed)
    Abstract [en]

    It is well known that the functorial equivalence between pairs (X, sigma), where X is a Riemann surface which admits an antiholomorphic involution (symmetry) sigma: X --> X, and real algebraic curves. We shall refer to such Riemann surfaces as real Riemann surfaces, following Klein's terminology. We consider the sets M-g(R) and M-g(2R) of real curves and :real hyperelliptic curves, respectively in the moduli space M-g of complex algebraic curves of genus g. In this paper we prove that any real hyperelliptic Riemann surface can be quasiconformally deformed, preserving the real and hyperelliptic character, to a real hyperelliptic Riemann surface (X, sigma), such that X admits a symmetry tau, where Fix (tau) is connected and non-separating. As a consequence, we obtain the connectedness of the sets M-g(2R)(subset of M-g) of all real hyperelliptic Riemann surfaces of genus g and M-g(R)(subset of M-g) of all real Riemann surfaces of given genus g using a procedure different from the one given by Seppala for M-g(2R) and Buser, Seppala and Silhol for M-g(R). A Riemann surface X is called a p-gonal Riemann surface, where p is a prime, if there exists a p-fold covering map from X onto the Riemann sphere. We prove ill this paper that the subset of real p-gonal Riemann surfaces, p greater than or equal to 3, is not a connected subset of M-g in general. This generalizes a result of Gross and Harris for real trigonal algebraic curves.

  • 14.
    Costa, A.F.
    et al.
    Departamento de Matemáticas, Facultad de Ciencias, Universidad Nacional de Educación Distancia (UNED), Senda del rey 9, 28040 Madrid, Spain.
    Izquierdo, Milagros
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
    Riera, G.
    Facultad de Matemáticas, Pontificia Universidad Católica de Chile, Avenida Vicuña Mackenna 4860, Santiago, Chile.
    One-dimensional Hurwitz spaces, modular curves, and real forms of Belyi meromorphic functions2008In: International journal of mathematics and mathematical sciences, ISSN 0161-1712, E-ISSN 1687-0425, Vol. 2008Article in journal (Refereed)
    Abstract [en]

    Hurwitz spaces are spaces of pairs (S, f) where S is a Riemann surface and f : S ? C^ a meromorphicfunction. In this work, we study 1-dimensional Hurwitz spaces HDp of meromorphic p-fold functions with four branched points, three of them fixed, the corresponding monodromy representation over each branched point is a product of (p - 1)/2 transpositions and the monodromy groupis the dihedral group Dp. We prove that the completion HDp of the Hurwitz space HDp is uniformized by a non-nomal index p + 1 subgroup of a triangular group with signature (0, [p, p, p]). We also establish the relation of the meromorphic covers with elliptic functions and show that HDp is aquotient of the upper half plane by the modular group G (2) n G0 (p). Finally, we study the real forms of the Belyi projection HDp ? C^ and show that there are two nonbicoformal equivalent such real forms which are topologically conjugated.

  • 15.
    Costa, Antonio F
    et al.
    UNED.
    Izquierdo, Milagros
    Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.
    Correction: Maximal order of automorphisms of trigonal Riemann surfaces (vol 323, pg 27, 2010)2011In: Journal of Algebra, ISSN 0021-8693, E-ISSN 1090-266X, Vol. 341, no 1, p. 313-314Article in journal (Refereed)
    Abstract [en]

    n/a

  • 16.
    Costa, Antonio F.
    et al.
    Departamento de Matemáticas Fundamentales, UNED, Spain.
    Izquierdo, Milagros
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.
    Equisymmetric strata of the singular locus of the moduli space of Riemann surfaces of genus 42010In: Geometry of Riemann Surfaces: proceedings of the Anogia conference to celebrate the 65th birthday of William J. Harvey / [ed] Frederick P. Gardiner, Gabino González-Diez, Christos Kourouniotis, Cambridge University Press, 2010, p. 120-138Chapter in book (Other academic)
    Abstract [en]

    Riemann surfaces is a thriving area of mathematics with applications to hyperbolic geometry, complex analysis, fractal geometry, conformal dynamics, discrete groups, geometric group theory, algebraic curves and their moduli, various kinds of deformation theory, coding, thermodynamic formalism, and topology of three-dimensional manifolds. This collection of articles, authored by leading authorities in the field, comprises 16 expository essays presenting original research and expert surveys of important topics related to Riemann surfaces and their geometry. It complements the body of recorded research presented in the primary literature by broadening, re-working and extending it in a more focused and less formal framework, and provides a valuable commentary on contemporary work in the subject. An introductory section sets the scene and provides sufficient background to allow graduate students and research workers from other related areas access to the field.

  • 17.
    Costa, Antonio F.
    et al.
    Departamento de Matemáticas Fundamentales, Facultad de Ciencias, UNED.
    Izquierdo, Milagros
    Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.
    Maximal order of automorphisms of trigonal Riemann surfaces2010In: Journal of Algebra, ISSN 0021-8693, E-ISSN 1090-266X, Vol. 323, no 1, p. 27-31Article in journal (Refereed)
    Abstract [en]

    In this paper we find the maximal order of an automorphism of a trigonal Riemann surface of genus g, g5. We find that this order is smaller for generic than for cyclic trigonal Riemann surfaces, showing that generic trigonal surfaces have “less symmetry” than cyclic trigonal surfaces. Finally we prove that the maximal order is attained for infinitely many genera in both the cyclic and the generic case.

  • 18.
    Costa, Antonio F.
    et al.
    Departamento de Matemáticas Fundamentales, Facultad de Ciencias, Universidad Nacional de Educacin a Distancia, 28040 Madrid, Spain.
    Izquierdo, Milagros
    Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.
    ON THE CONNECTEDNESS OF THE BRANCH LOCUS OF THE MODULI SPACE OF RIEMANN SURFACES OF GENUS 42010In: Glasgow Mathematical Journal, ISSN 0017-0895, E-ISSN 1469-509X, Vol. 52, p. 401-408Article in journal (Refereed)
    Abstract [en]

    Let g be an integer ≥ 3 and let θg = {X ∈ Mg|Aut(X) ≠ 1d}, where Mg denotes the moduli space of a compact Riemann surface. Using uniformization of Riemann surfaces by Fuchsian groups and the equisymmetric stratification of the branch locus of the moduli space we prove that the subloci corresponding to Riemann surfaces with automorphism groups isomorphic to cyclic groups of order 2 and 3 belongs to the same connected component. We also prove the connectedness of θg for g = 5, 6, 7 and 8 with the exception of the isolated points given by Kulkarni.

  • 19.
    Costa, Antonio F.
    et al.
    UNED, Madrid, Spain .
    Izquierdo, Milagros
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.
    On the existence of connected components of dimension one in the branch locus of moduli spaces of Riemann surfaces2012In: Mathematica Scandinavica, ISSN 0025-5521, E-ISSN 1903-1807, Vol. 111, no 1, p. 53-64Article in journal (Refereed)
    Abstract [en]

     Let g be an integer >= 3 and let B-g = {X is an element of mu(g) : Aut(X) not equal Id} be the branch locus of mu(g), where mu(g) denotes the moduli space of compact Riemann surfaces of genus g. The structure of B-g is of substantial interest because B-g corresponds to the singularities of the action of the modular group on the Teichmuller space of surfaces of genus g (see [14]).

    Kulkarni ([15], see also [13]) proved the existence of isolated points in the branch loci of the moduli spaces of Riemann surfaces. In this work we study the isolated connected components of dimension 1 in such loci. These isolated components of dimension one appear if the genus is g = p - 1 with p prime >= 11. We use uniformization by Fuchsian groups and the equisymmetric stratification of the branch loci.

  • 20.
    Costa, Antonio F.
    et al.
    Departamento de Matemáticas Fundamentales, Facultad de Ciencias, UNED, Madrid, Spain.
    Izquierdo, Milagros
    Linköping University, Department of Mathematics. Linköping University, Faculty of Science & Engineering.
    One-dimensional families of Riemann surfaces of genus g with 4g+4automorphims2018In: RACSAM, ISSN 1578-7303, Vol. 112, no 3, p. 623-631Article in journal (Refereed)
    Abstract [en]

    We prove that themaximal number ag+b of automorphisms of equisymmetric and

    complex-uniparametric families of Riemann surfaces appearing in all genera is 4g + 4. For

    each integer g ≥ 2 we find an equisymmetric complex-uniparametric family Ag of Riemann

    surfaces of genus g having automorphism group of order 4g + 4. For g ≡ −1mod 4 we

    present another uniparametric family Kg with automorphism group of order 4g + 4. The

    family Ag contains the Accola–Maclachlan surface and the family Kg contains the Kulkarni

    surface

  • 21.
    Costa, Antonio F.
    et al.
    Departamento de Matematicas Fundamentales, UNED.
    Izquierdo, Milagros
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.
    Parlier, Hugo
    Department of Mathematics, University of Fribourg, Switzerland.
    Connecting p-gonal loci in the compactification of moduli space2015In: Revista Matemática Complutense, ISSN 1139-1138, Vol. 28, no 2, p. 469-486Article in journal (Refereed)
    Abstract [en]

    Consider the moduli space M g of Riemann surfaces of genusg≥2 and its Deligne-Munford compactification M g ¯ . We are interested in the branch locus B g for g>2 , i.e., the subset of M g consisting of surfaces with automorphisms. It is well-known that the set of hyperelliptic surfaces (the hyperelliptic locus) is connected in M g but the set of (cyclic) trigonal surfaces is not. By contrast, we show that for g≥5 the set of (cyclic) trigonal surfaces is connected in M g ¯ . To do so we exhibit an explicit nodal surface that lies in the completion of every equisymmetric set of 3-gonal Riemann surfaces. For p>3 the connectivity of the p -gonal loci becomes more involved. We show that for p≥11 prime and genus g=p−1 there are one-dimensional strata of cyclic p -gonal surfaces that are completely isolated in the completion B g ¯ of the branch locus in M g ¯ .

  • 22.
    Costa, Antonio F.
    et al.
    Departamento de Matematicas Fundamentales, UNED.
    Izquierdo, Milagros
    Linköping University, Department of Mathematics. Linköping University, The Institute of Technology.
    Porto, Ana M.
    Departamento de Matematicas Fundamentales, UNED.
    Maximal and non-maximal NEC and Fuchsian groups uniformizing Klein and Riemann surfaces2014In: Riemann and Klein Surfaces, Automorphisms, Symmetries and Moduli Spaces / [ed] Milagros Izquierdo, S. Allen Broughton, Antonio F. Costa, Rubí E. Rodríguez, American Mathematical Society (AMS), 2014, Vol. 629, p. 107-118Chapter in book (Refereed)
  • 23.
    Costa, Antonio F.
    et al.
    Departamento de Matematicas Fundamentales, UNED.
    Izquierdo, Milagros
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.
    Porto, Ana M.
    Departamento de Matematicas Fundamentales, UNED.
    On the connectedness of the branch loci of moduli spaces of orientable Klein surfaces2015In: Geometriae Dedicata, ISSN 0046-5755, E-ISSN 1572-9168, Vol. 177, no 1, p. 149-164Article in journal (Refereed)
    Abstract [en]

    Let M K (g,+,k) be the moduli space of orientable Klein surfaces of genus g with k boundary components (see Alling and Greenleaf in Lecture notes in mathematics, vol 219. Springer, Berlin, 1971; Natanzon in Russ Math Surv 45(6):53–108, 1990). The space M K (g,+,k) has a natural orbifold structure with singular locus B K (g,+,k) . If g>2 or k>0 and 2g+k>3 the set B K (g,+,k) consists of the Klein surfaces admitting non-trivial symmetries and we prove that, in this case, the singular locus is connected.

  • 24.
    Costa, Antonio F.
    et al.
    Departamento de Matematicas Fundamentales, UNED.
    Izquierdo, Milagros
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
    Porto, Ana M.
    Departamento de Matematicas Fundamentales, UNED.
    On the connectedness of the branch locus of moduli space of hyperelliptic Klein surfaces with one boundary2017In: International Journal of Mathematics, ISSN 0129-167X, ISSN 0129-167X, Vol. 28, no 5, article id 1750038Article in journal (Refereed)
  • 25.
    Costa, Antonio F.
    et al.
    Departamento de Matematicas Fundamentales, UNED.
    Izquierdo, Milagros
    Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.
    Ying, Daniel
    Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.
    On cyclic p-gonal Riemann surfaces with several p-gonal morphisms2010In: Geometriae Dedicata, ISSN 0046-5755, E-ISSN 1572-9168, Vol. 147, no 1, p. 139-147Article in journal (Refereed)
    Abstract [en]

    Let p be a prime number, p > 2. A closed Riemann surface which can be realized as a p-sheeted covering of the Riemann sphere is called p-gonal, and such a covering is called a p-gonal morphism. If the p-gonal morphism is a cyclic regular covering, the Riemann surface is called a cyclic p-gonal Riemann surface. Accola showed that if the genus is greater than (p − 1)2 the p-gonal morphism is unique. Using the characterization of p-gonality by means of Fuchsian groups we show that there exists a uniparametric family of cyclic p-gonal Riemann surfaces of genus (p − 1)2 which admit two p-gonal morphisms. In this work we show that these uniparametric families are connected spaces and that each of them is the Riemann sphere without three points. We study the Hurwitz space of pairs (X, f), where X is a Riemann surface in one of the above families and f is a p-gonal morphism, and we obtain that each of these Hurwitz spaces is a Riemann sphere without four points.

  • 26.
    Costa, Antonio F
    et al.
    UNED.
    Izquierdo, Milagros
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
    Ying, Daniel
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
    On the family of cyclic trigonal Riemann surfaces of genus 4 with several trigonal morphisms2007In: Revista de la Real Academia de ciencias exactas, físicas y naturales. Serie A, Matematicas, ISSN 1578-7303, Vol. 101, no 1, p. 81-86Article in journal (Refereed)
    Abstract [en]

    A closed Riemann surface which is a 3-sheeted regular covering of the Riemann sphere is called cyclic trigonal, and such a covering is called a cyclic trigonal morphism. Accola showed that if the genus is greater or equal than 5 the trigonal morphism is unique. Costa-Izquierdo-Ying found a family of cyclic trigonal Riemann surfaces of genus 4 with two trigonal morphisms. In this work we show that this family is the Riemann sphere without three points. We also prove that the Hurwitz space of pairs (trigonal morphism, is the Riemann sphere with four punctures. Finally, we give the equations of the curves in the family.

     

     

     

     

     

  • 27.
    Estevez, Jose Luis
    et al.
    UNED, Madrid.
    Izquierdo, Milagros
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
    Non-normal pairs of non-Euclidean crystallographic groups2006In: Bulletin of the London Mathematical Society, ISSN 0024-6093, E-ISSN 1469-2120, Vol. 38, p. 113-123Article in journal (Refereed)
    Abstract [en]

    Let Gamma be a non-Euclidean crystallographic group. Gamma is said to be non-maximal if there exists a non-Euclidean crystallographic group Gamma' such that Gamma <= Gamma' and the dimension of the Teichmuller space of Gamma equals the dimension of the Teichmuller space of V. The full list Of such pairs of groups is computed in the case when Gamma is non-normal in Gamma'. The corresponding problem for Fuchsian groups was solved by Singerman.

  • 28.
    Hidalgo, Ruben A.
    et al.
    University of Tecn Federico Santa Maria, Chile .
    Izquierdo, Milagros
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.
    ON THE CONNECTIVITY OF THE BRANCH LOCUS OF THE SCHOTTKY SPACE2014In: Annales Academiae Scientiarum Fennicae Mathematica, ISSN 1239-629X, E-ISSN 1798-2383, Vol. 39, no 2, p. 635-654Article in journal (Refereed)
    Abstract [en]

    Let M be a handlebody of genus g greater than= 2. The space T(M), that parametrizes marked Kleinian structures on M up to isomorphisms, can be identified with the space MSg, of marked Schottky groups of rank g, so it carries a structure of complex manifold of finite dimension 3(g - 1). The space M(M) parametrizing Kleinian structures on M up to isomorphisms, can be identified with S-g, the Schottky space of rank g, and it carries the structure of a complex orbifold. In these identifications, the projection map pi: T(M) -greater than M(M) corresponds to the map from MSg, onto S-g that forgets the marking. In this paper we observe that the singular locus B(M) of M(M), that is, the branch locus of pi, has (i) exactly two connected components for g = 2, (ii) at most two connected components for g greater than= 4 even, and (iii) M(M) is connected for g greater than= 3 odd.

  • 29.
    Izquierdo, Milagros
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
    Cyclic p-gonal Riemann surfaces with 2 p-gonal morphisms2007In: Geometry of Riemann Surfaces,2007, 2007Conference paper (Other academic)
  • 30.
    Izquierdo, Milagros
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
    Groups Actions on Surfaces of Genus 42006In: SiGMAC06,2006, 2006Conference paper (Other academic)
  • 31.
    Izquierdo, Milagros
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
    Kombinatoriska metoder för algebraiska kurvor2004In: Workshop i tillämpad matematik,2004, 2004Conference paper (Other academic)
  • 32.
    Izquierdo, Milagros
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
    La Banda de Moebius2007In: Arte y Matemáticas, Madrid: Pub. UNED , 2007Chapter in book (Other academic)
    Abstract [en]

      

  • 33.
    Izquierdo, Milagros
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
    La banda de Möbius2003In: Arte y Matematicas, Publicaciones de la UNED , 2003Chapter in book (Other academic)
  • 34.
    Izquierdo, Milagros
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
    La Banda de Möbius2003In: Summer School in Art and Mathematics,2003, 2003Conference paper (Other academic)
  • 35.
    Izquierdo, Milagros
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
    Ovals of real cyclic p-gonal Riemann surfaces2003In: Joint meeting of the American Mathematical Society and the Spanish Mathematical Society,2003, 2003Conference paper (Other academic)
  • 36.
    Izquierdo, Milagros
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
    Ovals of real trigonal Riemann surfaces2003In: Joint meeting of the AMS - MAA,2003, 2003Conference paper (Other academic)
  • 37.
    Izquierdo, Milagros
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
    Symmetries of real cyclic p-gonal Riemann surfaces2003In: Discrete groups, Riemann surfaces and conformal geometry,2003, 2003Conference paper (Other academic)
  • 38.
    Izquierdo, Milagros
    et al.
    Linköping University, Department of Mathematics. Linköping University, The Institute of Technology.
    Broughton, S AllenRose-Hulman Institute of Technology, USA.Costa, Antonio F.Departamento de Matematicas Fundamentales, Universidad Nacional de Educación a Distancia, Madrid, Spain.Rodriguez, Rubi E.Departamento de Matemática, Universidad de la Frontera, Temuco, Chile.
    Riemann and Klein surfaces, automorphisms, symmetries and moduli spaces: conference in honor of Emilio Bujalance on Riemann and Klein surfaces, symmetries and moduli spaces, June 24-28, 2013, Linköping University, Linköping, Sweden2014Collection (editor) (Refereed)
  • 39.
    Izquierdo, Milagros
    et al.
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
    Costa, Antonio F
    Symmetries of real cyclic p-gonal Riemann surfaces2004In: Pacific Journal of Mathematics, ISSN 0030-8730, E-ISSN 1945-5844, Vol. 213, no 2, p. 231-243Article in journal (Refereed)
    Abstract [en]

    A closed Riemann surface X which can be realised as a p-sheeted covering of the Riemann sphere is called p-gonal, and such a covering is called a p-gonal morphism. A p-gonal Riemann surface is called real p-gonal if there is an ant iconformal involution (symmetry) σ of X commuting with the p-gonal morphism. If the p-gonal morphism is a cyclic regular covering the Riemann surface is called real cyclic p-gonal, otherwise it is called real generic p-gonal. The species of the symmetry σ is the number of connected components of the fixed point set Fix (σ) and the orientability of the Klein surface X/〈σ〉. In this paper we find the species for the possible symmetries of real cyclic p-gonal Riemann surfaces by means of Fuchsian and NEC groups.

  • 40.
    Izquierdo, Milagros
    et al.
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
    Estevez, Jose Luis
    On non-normal pairs of NEC groups2005In: Joint Mathematics Meeting AMS-MAA,2005, 2005Conference paper (Refereed)
  • 41.
    Izquierdo, Milagros
    et al.
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
    Johansson, KarinLinköping University, Department of Computer and Information Science, The Division of Statistics and Machine Learning. Linköping University, Faculty of Science & Engineering.
    Meeting of the Catalan, Spanish, Swedish Math Societies (CAT‐SP‐SW‐MATH)2017Conference proceedings (editor) (Other academic)
    Abstract [en]

    A joint Meeting of the Catalan, Spanish, Swedish Math Societies (CAT-SP-SW-MATH) will be held in Umeå (Sweden) from 12th to 15th June 2017.

    The meeting is a symposium devoted to mathematics at large.

    The conference is thought as a meeting point between the different areas of mathematics and its applications.

    The programme will consist of several plenary lectures, covering a wide range of areas of mathematics, and special sessions devoted to a single topic or area of mathematics.

    The venue of the conference will be the Department of Mathematics and Mathematical Statistics of Umeå University.

    Welcome!

    Milagros Izquierdo (Svenska matematikersamfundet)

    Xavier Jarque (Societat Catalana de Matemàtiques)

    Francisco José Marcellán (Real Sociedad Matemática Española)

  • 42.
    Izquierdo, Milagros
    et al.
    Linköping University, Department of Mathematics. Linköping University, Faculty of Science & Engineering.
    Stokes, Klara
    Högskolan i Skövde.
    Isometric Point-Circle Configurations on Surfaces from Uniform Maps2016In: Springer Proceedings in Mathematics and Statistics, ISSN 2194-1009, Vol. 159, p. 201-212Article in journal (Refereed)
    Abstract [en]

    We embed neighborhood geometries of graphs on surfaces as point-circle configurations. We give examples coming from regular maps on surfaces with a maximum number of automorphisms for their genus, and survey geometric realization of pentagonal geometries coming from Moore graphs. An infinite family of point-circle v4'>v4v4 configurations on p-gonal surfaces with two p-gonal morphisms is given. The image of these configurations on the sphere under the two p-gonal morphisms is also described.

  • 43.
    Izquierdo, Milagros
    et al.
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
    Tony, Shaska
    Oakland University, Michigan, USA.
    Cyclic Curves over the reals2015In: Advances on Superelliptic Curves and Their Applications / [ed] Lubjana Beshaj, Tony Shaska, Eustrat Zhupa, Amsterdam: IOS Press, 2015, p. 70-83Chapter in book (Refereed)
    Abstract [en]

    In this paper we study the automorphism groups of real curves admitting a regular meromorphic function f of degree p, so called real cyclic p-gonal curves. When p = 2 the automorphism groups of real hyperelliptic curves where given by Bujalance et al. in [4].

  • 44.
    Izquierdo, Milagros
    et al.
    Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.
    Ying , Daniel
    Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.
    Equisymmetric Strata of the Moduli Space of Cyclic Trigonal Riemann Surfaces of Genus 42009In: GLASGOW MATHEMATICAL JOURNAL, ISSN 0017-0895 , Vol. 51, p. 19-29Article in journal (Refereed)
    Abstract [en]

    A closed Riemann surface which can be realized as a three-sheeted covering of the Riemann sphere is called trigonal, and such a covering is called a trigonal morphism. If the trigonal morphism is a cyclic regular covering, the Riemann surface is called a cyclic trigonal Riemann Surface. Using the characterization of cyclic trigonality by Fuchsian groups, we find the structure of the space of cyclic trigonal Riemann surfaces of genus 4.

  • 45.
    Izquierdo, Milagros
    et al.
    Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.
    Ying, Daniel
    Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.
    On the space of cyclic trigonal Riemann surfaces of genus 42007In: Groups St Andrews 2005 Volume 2 / [ed] C. M. Campbell, M. R. Quick, E. F. Robertson, G. C. Smith, Cambridge, UK: Cambridge University Press, 2007, 1, p. 504-516Chapter in book (Other academic)
    Abstract [en]

        'Groups St Andrews 2005' was held in the University of St Andrews in August 2005 and this first volume of a two-volume book contains selected papers from the international conference. Four main lecture courses were given at the conference, and articles based on their lectures form a substantial part of the Proceedings. This volume contains the contributions by Peter Cameron (Queen Mary, London) and Rostislav Grogorchuk (Texas A&M, USA).  Apart from the main speakers, refereed survey and research articles were contributed by other conference participants. Arranged in alphabetical order, these articles cover a wide spectrum of modern group theory. The regular Proceedings of Groups St Andrews conferences have provided snapshots of the state of research in group theory throughout the past 25 years. Earlier volumes have had a major impact on the development of group theory and it is anticipated that this volume will be equally important.

  • 46.
    Izquierdo, Milagros
    et al.
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
    Ying, Daniel
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
    Trigonal Riemann surfaces of genus 42005In: XII Nevanlinna Colloquium,2005, 2005Conference paper (Other academic)
  • 47.
    Izquierdo, Milagros
    et al.
    Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.
    Ying, Daniel
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
    Costa, Antonio F
    On Riemann surfaces with non-unique cyclic trigonal morphism2005In: Manuscripta mathematica, ISSN 0025-2611, E-ISSN 1432-1785, Vol. 118, p. 443-453Article in journal (Refereed)
  • 48.
    Izquierdo, Milagros
    et al.
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
    Ying, Daniel
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
    Costa, Antonio F
    Trigonal Riemann surfaces with non-unique morphisms2005In: Sectional Meeting AMS,2005, 2005Conference paper (Refereed)
  • 49.
    Stokes, Klara
    et al.
    University of Skovde, Sweden.
    Izquierdo, Milagros
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
    Geometric point-circle pentagonal geometries from Moore graphs2016In: Ars Mathematica Contemporanea, ISSN 1855-3966, Vol. 11, no 1, p. 215-229Article in journal (Refereed)
    Abstract [en]

    We construct isometric point-circle configurations on surfaces from uniform maps. This gives one geometric realisation in terms of points and circles of the Desargues configuration in the real projective plane, and three distinct geometric realisations of the pentagonal geometry with seven points on each line and seven lines through each point on three distinct dianalytic surfaces of genus 57. We also give a geometric realisation of the latter pentagonal geometry in terms of points and hyperspheres in 24 dimensional Euclidean space. From these, we also obtain geometric realisations in terms of points and circles (or hyperspheres) of pentagonal geometries with k circles (hyperspheres) through each point and k 1 points on each circle (hypersphere).

1 - 49 of 49
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