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Broughton, S. A., Costa, A. F. & Izquierdo, M. (2024). One dimensional equisymmetric strata in moduli space with genus 1 quotient surfaces. Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, 118(1), Article ID 21.
Open this publication in new window or tab >>One dimensional equisymmetric strata in moduli space with genus 1 quotient surfaces
2024 (English)In: Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, ISSN 1578-7303, Vol. 118, no 1, article id 21Article in journal (Refereed) Published
Abstract [en]

The complex orbifold structure of the moduli space of Riemann surfaces of genus g (g≥2) produces a stratification into complex subvarieties named equisymmetric strata. Each equisymmetric stratum is formed by the surfaces where the group of automorphisms acts in a topologically equivalent way. The Riemann surfaces in the equisymmetric strata of dimension one are of two structurally different types. Type 1 equisymmetric strata correspond to Riemann surfaces where the group of automorphisms produces a quotient surface of genus zero, while those of Type 2 appear when such a quotient is a surface of genus one. Type 1 equisymmetric strata have been extensively studied by the authors of the present work in a previous recent paper, we now focus on Type 2 strata. We first establish the existence of such strata and their frequency of occurrence in moduli spaces. As a main result we obtain a complete description of Type 2 strata as coverings of the sphere branched over three points (Belyi curves) and where certain isolated points (punctures) have to be eliminated. Finally, we study in detail the doubly infinite family of Type 2 strata whose automorphism groups have order the product of two primes.

Place, publisher, year, edition, pages
SPRINGER-VERLAG ITALIA SRL, 2024
Keywords
Riemann surface, Moduli space, Automorphism group
National Category
Mathematics
Identifiers
urn:nbn:se:liu:diva-199034 (URN)10.1007/s13398-023-01520-9 (DOI)001096335300001 ()
Available from: 2023-11-08 Created: 2023-11-08 Last updated: 2023-12-06
Izquierdo, M., Jones, G. A. & Reyes-Carocca, S. (2021). Groups of Automorphisms of Riemann Surfaces and Maps of Genus p+1 Where p is Prime. Annales Fennici Mathematici, 46(2), 839-867
Open this publication in new window or tab >>Groups of Automorphisms of Riemann Surfaces and Maps of Genus p+1 Where p is Prime
2021 (English)In: Annales Fennici Mathematici, ISSN 2737-0690, Vol. 46, no 2, p. 839-867Article in journal (Refereed) Published
Abstract [en]

We classify compact Riemann surfaces of genus g, where g−1 is a prime p, which have a group of automorphisms of order ρ(g−1)for some integer ρ≥1, and determine isogeny decompositions of the corresponding Jacobian varieties. This extends results of Belolipetzky and the second author for ρ>6, and of the first and third authors for ρ= 3, 4, 5 and 6. As a corollary we classify the orientably regular hypermaps (including maps) of genus p+1, together with the non-orientable regular hypermaps of characteristic −p, with automorphism group of order divisible by the prime p; this extends results of Conder, Širáň and Tucker for maps.

Place, publisher, year, edition, pages
The Finnish Mathematical Society, 2021
Keywords
Compact Riemann surface, automorphism group, finite group, Jacobian, map, hypermap, dessin d'enfant
National Category
Geometry
Identifiers
urn:nbn:se:liu:diva-178382 (URN)
Available from: 2021-08-19 Created: 2021-08-19 Last updated: 2022-06-17Bibliographically approved
Izquierdo, M., Reyes-Carocca, S. & Rojas, A. (2021). On families of Riemann surfaces with automorphisms. Journal of Pure and Applied Algebra, 225(10), Article ID 106704.
Open this publication in new window or tab >>On families of Riemann surfaces with automorphisms
2021 (English)In: Journal of Pure and Applied Algebra, ISSN 0022-4049, E-ISSN 1873-1376, Vol. 225, no 10, article id 106704Article in journal (Refereed) Published
Abstract [en]

In this article we determine the maximal possible order of the automorphism group 18 of the form ag + b, where a and b are integers, of a complex three and four- 19 dimensional family of compact Riemann surfaces of genus g, appearing for all genus.In addition, we construct and describe explicit complex three and four-dimensional 20 families possessing these maximal numbers of automorphisms.

Place, publisher, year, edition, pages
Elsevier, 2021
National Category
Natural Sciences Mathematics
Identifiers
urn:nbn:se:liu:diva-173265 (URN)10.1016/j.jpaa.2021.106704 (DOI)000647700700022 ()
Note

Funding: Redes Grant [2017-170071]; FONDECYTComision Nacional de Investigacion Cientifica y Tecnologica (CONICYT)CONICYT FONDECYT [11180024, 1190991, 1180073]

Available from: 2021-02-11 Created: 2021-02-11 Last updated: 2023-02-10Bibliographically approved
Izquierdo, M., Jones, G. A. & Reyes Carocca, S. (2020). Groups of automorphisms of Riemann surfaces and maps of genus p + 1 where p is prime. Annales Academiæ Scientiarum Fennicæ Mathematica, 46(2), 839-867
Open this publication in new window or tab >>Groups of automorphisms of Riemann surfaces and maps of genus p + 1 where p is prime
2020 (English)In: Annales Academiæ Scientiarum Fennicæ Mathematica, ISSN 1239-629X, Vol. 46, no 2, p. 839-867Article in journal (Refereed) Published
Abstract [en]

We classify compact Riemann surfaces of genus g, where g−1 is a prime p, whichhave a group of automorphisms of order ρ(g−1) for some integer ρ ≥ 1, and determine isogeny decompositions of the corresponding Jacobian varieties. This extends results of Belolipetzky and the second author for ρ > 6, and of the first and third authors for ρ = 3,4,5 and 6. As a corollary we classify the orientably regular hypermaps (including maps) of genus p +1, together with the non-orientable regular hypermaps of characteristic − p, with automorphism group of order divisible by the prime p; this extends results of Conder, Širáň and Tucker for maps.

Place, publisher, year, edition, pages
Helsinki, Finland: Academia Scientiarum Fennica, 2020
Keywords
Compact Riemann surface, automorphism group, finite group, Jacobian, map, hypermap, dessin d’enfant
National Category
Mathematical Analysis
Identifiers
urn:nbn:se:liu:diva-172024 (URN)10.5186/aasfm.2021.4649 (DOI)2-s2.0-85114837063 (Scopus ID)
Available from: 2020-12-18 Created: 2020-12-18 Last updated: 2022-11-28
Bujalance, E., Conder, M., Costa, A. F. & Izquierdo, M. (2019). On regular dessins d'enfants with 4g automorphisms and a curve of Wiman. Contemporary Mathematics, 724, 225-233
Open this publication in new window or tab >>On regular dessins d'enfants with 4g automorphisms and a curve of Wiman
2019 (English)In: Contemporary Mathematics, ISSN 0271-4132, E-ISSN 1098-3627, Vol. 724, p. 225-233Article in journal (Refereed) Published
Place, publisher, year, edition, pages
Providence: American Mathematical Society (AMS), 2019
National Category
Mathematical Analysis
Identifiers
urn:nbn:se:liu:diva-160691 (URN)
Available from: 2019-10-02 Created: 2019-10-02 Last updated: 2020-11-09Bibliographically approved
Artal, E., Costa, A. F. & Izquierdo, M. (2018). Correction: Professor Maria Teresa Lozano and universal links (vol 87, pg 441, 1987). REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS, 112(3), 621-621
Open this publication in new window or tab >>Correction: Professor Maria Teresa Lozano and universal links (vol 87, pg 441, 1987)
2018 (English)In: 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) Published
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.

Place, publisher, year, edition, pages
Springer, 2018
National Category
Mathematics
Identifiers
urn:nbn:se:liu:diva-149691 (URN)10.1007/s13398-017-0468-6 (DOI)000437016800002 ()
Available from: 2018-07-24 Created: 2018-07-24 Last updated: 2018-08-14
Izquierdo, M. & Hidalgo, R. (2018). On the connectedness of the Branch locus of the Schottky space. Albanian Journal of Mathematics, 12(1), 131-136
Open this publication in new window or tab >>On the connectedness of the Branch locus of the Schottky space
2018 (English)In: Albanian Journal of Mathematics, ISSN 1930-1235, E-ISSN 1930-1235, Vol. 12, no 1, p. 131-136Article in journal (Refereed) Published
Abstract [en]

Schottky space Sg is the space that parametrizes PSL2(C)-conjugacy classes of Schottky groups of rank g ≥ 2. The branch locus Bg consists of the conjugacy classes of those Schottky groups which are a finite index proper subgroup of some Kleinian group. In a previous paper we observed that Bg was connected for g ≥ 3 odd and that it has at most two components for g ≥ 4 even. In this short note, we observe that Bg is always connected.

Place, publisher, year, edition, pages
White Lake, MI United States: Aulonna Press, 2018
National Category
Natural Sciences Geometry
Identifiers
urn:nbn:se:liu:diva-160690 (URN)
Available from: 2019-10-02 Created: 2019-10-02 Last updated: 2019-10-08Bibliographically approved
Costa, A. F. & Izquierdo, M. (2018). One-dimensional families of Riemann surfaces of genus g with 4g+4automorphims. RACSAM, 112(3), 623-631
Open this publication in new window or tab >>One-dimensional families of Riemann surfaces of genus g with 4g+4automorphims
2018 (English)In: RACSAM, ISSN 1578-7303, Vol. 112, no 3, p. 623-631Article in journal (Refereed) Published
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

Place, publisher, year, edition, pages
Springer Berlin/Heidelberg, 2018
Keywords
Riemann surface, Automorphism group, Fuchsian group
National Category
Mathematics
Identifiers
urn:nbn:se:liu:diva-140428 (URN)10.1007/s13398-017-0429-0 (DOI)000437016800003 ()
Note

Funding agencies: Ministerio de Economia y Competitividad [MTM2014-55812-P]

Available from: 2017-09-04 Created: 2017-09-04 Last updated: 2018-08-14Bibliographically approved
Artal, E., Costa, A. F. & Izquierdo, M. (2018). Professor Maria Teresa Lozano and universal links. REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS, 112(3), 615-620
Open this publication in new window or tab >>Professor Maria Teresa Lozano and universal links
2018 (English)In: 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, Editorial material (Other academic) Published
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

Place, publisher, year, edition, pages
SPRINGER-VERLAG ITALIA SRL, 2018
National Category
Mathematics
Identifiers
urn:nbn:se:liu:diva-149690 (URN)10.1007/s13398-017-0446-z (DOI)000437016800001 ()
Available from: 2018-07-24 Created: 2018-07-24 Last updated: 2018-08-14
Artal, E., Costa, A. F. & Izquierdo, M. (Eds.). (2018). Special Issue: Dedicated to María Teresa Lozano conmemorating her 70th Birthday. Springer
Open this publication in new window or tab >>Special Issue: Dedicated to María Teresa Lozano conmemorating her 70th Birthday
2018 (English)Collection (editor) (Refereed)
Place, publisher, year, edition, pages
Springer, 2018. p. 914
Series
Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, ISSN 1578-7303, E-ISSN 1579-1505 ; 112(3)
National Category
Mathematics
Identifiers
urn:nbn:se:liu:diva-150155 (URN)
Available from: 2018-08-14 Created: 2018-08-14 Last updated: 2018-08-14Bibliographically approved
Organisations
Identifiers
ORCID iD: ORCID iD iconorcid.org/0000-0002-9557-9566

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