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Ying , Daniel
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Publications (10 of 11) Show all publications
Costa, A. F., Izquierdo, M. & Ying, D. (2010). On cyclic p-gonal Riemann surfaces with several p-gonal morphisms. Geometriae Dedicata, 147(1), 139-147.
Open this publication in new window or tab >>On cyclic p-gonal Riemann surfaces with several p-gonal morphisms
2010 (English)In: Geometriae Dedicata, ISSN 0046-5755, E-ISSN 1572-9168, Vol. 147, no 1, 139-147 p.Article in journal (Refereed) Published
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.

Place, publisher, year, edition, pages
Springer Berlin/Heidelberg, 2010
Keyword
p-Gonal Riemann surface - Hurwitz space - Algebraic complex curve
National Category
Mathematics
Identifiers
urn:nbn:se:liu:diva-52167 (URN)10.1007/s10711-009-9444-4 (DOI)
Note

The original publication is available at www.springerlink.com: Antonio F. Costa, Milagros Izquierdo and Daniel Ying, On cyclic p-gonal Riemann surfaces with several p-gonal morphisms, 2009, Geometriae Dedicata. http://dx.doi.org/10.1007/s10711-009-9444-4 Copyright: Springer Science Business Media http://www.springerlink.com/

Available from: 2009-12-08 Created: 2009-12-08 Last updated: 2017-12-12
Izquierdo, M. & Ying , D. (2009). Equisymmetric Strata of the Moduli Space of Cyclic Trigonal Riemann Surfaces of Genus 4. GLASGOW MATHEMATICAL JOURNAL, 51, 19-29.
Open this publication in new window or tab >>Equisymmetric Strata of the Moduli Space of Cyclic Trigonal Riemann Surfaces of Genus 4
2009 (English)In: GLASGOW MATHEMATICAL JOURNAL, ISSN 0017-0895 , Vol. 51, 19-29 p.Article in journal (Refereed) Published
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.

National Category
Mathematics
Identifiers
urn:nbn:se:liu:diva-16518 (URN)10.1017/S0017089508004497 (DOI)
Note
Original Publication: Milagros Izquierdo and Daniel Ying, Equisymmetric Strata of the Moduli Space of Cyclic Trigonal Riemann Surfaces of Genus 4, 2009, GLASGOW MATHEMATICAL JOURNAL, (51), 19-29. http://dx.doi.org/10.1017/S0017089508004497 Copyright: Cambridge University Press http://www.cambridge.org/uk/ Available from: 2009-01-30 Created: 2009-01-30 Last updated: 2015-03-09Bibliographically approved
Costa, A. F., Izquierdo, M. & Ying, D. (2007). On the family of cyclic trigonal Riemann surfaces of genus 4 with several trigonal morphisms. Revista de la Real Academia de ciencias exactas, físicas y naturales. Serie A, Matematicas, 101(1), 81-86.
Open this publication in new window or tab >>On the family of cyclic trigonal Riemann surfaces of genus 4 with several trigonal morphisms
2007 (English)In: Revista de la Real Academia de ciencias exactas, físicas y naturales. Serie A, Matematicas, ISSN 1578-7303, Vol. 101, no 1, 81-86 p.Article in journal (Refereed) Published
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.

 

 

 

 

 

National Category
Mathematics
Identifiers
urn:nbn:se:liu:diva-37190 (URN)33899 (Local ID)33899 (Archive number)33899 (OAI)
Note
Original Publication: Antonio F Costa, Milagros Izquierdo and Daniel Ying, On the family of cyclic trigonal Riemann surfaces of genus 4 with several trigonal morphisms, 2007, Revista de la Real Academia de ciencias exactas, físicas y naturales. Serie A, Matematicas, (101), 1, 81-86. Copyright: Real Academia de Ciencias, Espana Available from: 2009-10-10 Created: 2009-10-10 Last updated: 2015-03-09
Izquierdo, M. & Ying, D. (2007). On the space of cyclic trigonal Riemann surfaces of genus 4 (1ed.). In: C. M. Campbell, M. R. Quick, E. F. Robertson, G. C. Smith (Ed.), Groups St Andrews 2005 Volume 2: (pp. 504-516). Cambridge, UK: Cambridge University Press.
Open this publication in new window or tab >>On the space of cyclic trigonal Riemann surfaces of genus 4
2007 (English)In: 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, 504-516 p.Chapter 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.

Place, publisher, year, edition, pages
Cambridge, UK: Cambridge University Press, 2007 Edition: 1
Series
London Mathematical Society. Lecture Note Series, ISSN 0076-0552 ; 340
National Category
Mathematics Algebra and Logic
Identifiers
urn:nbn:se:liu:diva-30856 (URN)10.1017/CBO9780511721205.015 (DOI)16515 (Local ID)9780521694704 (ISBN)16515 (Archive number)16515 (OAI)
Available from: 2009-10-09 Created: 2009-10-09 Last updated: 2015-03-09Bibliographically approved
Ying, D. (2006). On the Moduli Space of Cyclic Trigonal Riemann Surfaces of Genus 4. (Doctoral dissertation). : Matematiska institutionen.
Open this publication in new window or tab >>On the Moduli Space of Cyclic Trigonal Riemann Surfaces of Genus 4
2006 (English)Doctoral thesis, monograph (Other academic)
Abstract [en]

A closed Riemann surface which can be realized as a 3-sheeted covering of the Riemann sphere is called trigonal, and such a covering is called a trigonal morphism. Accola showed that the trigonal morphism is unique for Riemann surfaces of genus g ≥ 5. This thesis characterizes the cyclic trigonal Riemann surfaces of genus 4 with non-unique trigonal morphism using the automorphism groups of the surfaces. The thesis shows that Accola’s bound is sharp with the existence of a uniparametric family of cyclic trigonal Riemann surfaces of genus 4 having several trigonal morphisms. The structure of the moduli space of trigonal Riemann surfaces of genus 4 is also characterized.

Finally, by using the same technique as in the case of cyclic trigonal Riemann surfaces of genus 4, we are able to deal with p-gonal Riemann surfaces and show that Accola’s bound is sharp for p-gonal Riemann surfaces. Furthermore, we study families of p-gonal Riemann surfaces of genus (p − 1)2 with two p-gonal morphisms, and describe the structure of their moduli space.

Place, publisher, year, edition, pages
Matematiska institutionen, 2006. 123 p.
Series
Linköping Studies in Science and Technology. Dissertations, ISSN 0345-7524 ; 1060
Keyword
Riemann surface, Riemann sphere, Trigonal morphism
National Category
Mathematics
Identifiers
urn:nbn:se:liu:diva-8237 (URN)91-85643-38-6 (ISBN)
Public defence
2006-12-14, Nobel, Hus B, Campus Valla, Linköpings universitet, Linköping, 10:15 (English)
Opponent
Supervisors
Available from: 2007-02-01 Created: 2007-02-01 Last updated: 2015-03-09
Izquierdo, M., Ying, D. & Costa, A. F. (2005). On Riemann surfaces with non-unique cyclic trigonal morphism. Manuscripta mathematica, 118, 443-453.
Open this publication in new window or tab >>On Riemann surfaces with non-unique cyclic trigonal morphism
2005 (English)In: Manuscripta mathematica, ISSN 0025-2611, E-ISSN 1432-1785, Vol. 118, 443-453 p.Article in journal (Refereed) Published
National Category
Mathematics
Identifiers
urn:nbn:se:liu:diva-22659 (URN)10.1007/s00229-005-0593-y (DOI)1946 (Local ID)1946 (Archive number)1946 (OAI)
Available from: 2009-10-07 Created: 2009-10-07 Last updated: 2017-12-13
Izquierdo, M. & Ying, D. (2005). Trigonal Riemann surfaces of genus 4. In: XII Nevanlinna Colloquium,2005. .
Open this publication in new window or tab >>Trigonal Riemann surfaces of genus 4
2005 (English)In: XII Nevanlinna Colloquium,2005, 2005Conference paper, Published paper (Other academic)
National Category
Mathematics
Identifiers
urn:nbn:se:liu:diva-30865 (URN)16525 (Local ID)16525 (Archive number)16525 (OAI)
Available from: 2009-10-09 Created: 2009-10-09 Last updated: 2015-03-09
Izquierdo, M., Ying, D. & Costa, A. F. (2005). Trigonal Riemann surfaces with non-unique morphisms. In: Sectional Meeting AMS,2005. .
Open this publication in new window or tab >>Trigonal Riemann surfaces with non-unique morphisms
2005 (English)In: Sectional Meeting AMS,2005, 2005Conference paper, Published paper (Refereed)
National Category
Mathematics
Identifiers
urn:nbn:se:liu:diva-30863 (URN)16523 (Local ID)16523 (Archive number)16523 (OAI)
Available from: 2009-10-09 Created: 2009-10-09 Last updated: 2015-03-09
Ying, D. (2004). Cyclic Trigonal Riemann Surfaces of Genus 4. (Licentiate dissertation). : Matematiska institutionen.
Open this publication in new window or tab >>Cyclic Trigonal Riemann Surfaces of Genus 4
2004 (English)Licentiate thesis, monograph (Other academic)
Abstract [en]

A closed Riemann surface which can be realized as a 3-sheeted covering of the Riemann sphere is called trigonal, and such a covering is called a trigonal morphism. Accola showed that the trigonal morphism is unique for Riemann surfaces of genus g ≥ 5. This thesis will characterize the Riemann surfaces of genus 4 wiht non-unique trigonal morphism. We will describe the structure of the space of cyclic trigonal Riemann surfaces of genus 4.

Place, publisher, year, edition, pages
Matematiska institutionen, 2004. 54 p.
Series
Linköping Studies in Science and Technology. Thesis, ISSN 0280-7971 ; 1125
Keyword
Riemann surface, trigonal morphism, Accola, genus 4
National Category
Mathematics
Identifiers
urn:nbn:se:liu:diva-5678 (URN)91-85295-68-X (ISBN)
Presentation
2004-11-10, 00:00 (English)
Note
Report code: LiU-Tek-Lic-2004:54. The electronic version of the printed licentiate thesis is a corrected version where errors in the calculations have been corrected. See Errata below for a list of corrections.Available from: 2004-11-23 Created: 2004-11-23 Last updated: 2009-06-09
Ying, D. (2004). Kubiska riemannytor. In: Workshop i tillämpad matematik,2004. .
Open this publication in new window or tab >>Kubiska riemannytor
2004 (Swedish)In: Workshop i tillämpad matematik,2004, 2004Conference paper, Published paper (Other academic)
National Category
Mathematics
Identifiers
urn:nbn:se:liu:diva-23216 (URN)2628 (Local ID)2628 (Archive number)2628 (OAI)
Available from: 2009-10-07 Created: 2009-10-07
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