A Universal Genus-Two Curve from Siegel Modular Forms
Let p be any point in the moduli space of genus-two curves M2 and K its field of moduli. We provide a universal equation of a genus-two curve Cα,β defined over K(α,β), corresponding to p, where α and β satisfy a quadratic α²+bβ²=c such that b and c are given in terms of ratios of Siegel modular form...
Gespeichert in:
| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Datum: | 2017 |
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | English |
| Veröffentlicht: |
Інститут математики НАН України
2017
|
| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/149268 |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | A Universal Genus-Two Curve from Siegel Modular Forms / A. Malmendier, T. Shaska // Symmetry, Integrability and Geometry: Methods and Applications. — 2017. — Т. 13. — Бібліогр.: 19 назв. — англ. |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
nasplib_isofts_kiev_ua-123456789-149268 |
|---|---|
| record_format |
dspace |
| spelling |
Malmendier, A. Shaska, T. 2019-02-19T19:32:49Z 2019-02-19T19:32:49Z 2017 A Universal Genus-Two Curve from Siegel Modular Forms / A. Malmendier, T. Shaska // Symmetry, Integrability and Geometry: Methods and Applications. — 2017. — Т. 13. — Бібліогр.: 19 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 14H10; 14H45 DOI:10.3842/SIGMA.2017.089 https://nasplib.isofts.kiev.ua/handle/123456789/149268 Let p be any point in the moduli space of genus-two curves M2 and K its field of moduli. We provide a universal equation of a genus-two curve Cα,β defined over K(α,β), corresponding to p, where α and β satisfy a quadratic α²+bβ²=c such that b and c are given in terms of ratios of Siegel modular forms. The curve Cα,β is defined over the field of moduli K if and only if the quadratic has a K-rational point (α,β). We discover some interesting symmetries of the Weierstrass equation of Cα,β. This extends previous work of Mestre and others. This paper is a contribution to the Special Issue on Modular Forms and String Theory in honor of Noriko Yui. The full collection is available at http://www.emis.de/journals/SIGMA/modular-forms.html. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications A Universal Genus-Two Curve from Siegel Modular Forms Article published earlier |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
A Universal Genus-Two Curve from Siegel Modular Forms |
| spellingShingle |
A Universal Genus-Two Curve from Siegel Modular Forms Malmendier, A. Shaska, T. |
| title_short |
A Universal Genus-Two Curve from Siegel Modular Forms |
| title_full |
A Universal Genus-Two Curve from Siegel Modular Forms |
| title_fullStr |
A Universal Genus-Two Curve from Siegel Modular Forms |
| title_full_unstemmed |
A Universal Genus-Two Curve from Siegel Modular Forms |
| title_sort |
universal genus-two curve from siegel modular forms |
| author |
Malmendier, A. Shaska, T. |
| author_facet |
Malmendier, A. Shaska, T. |
| publishDate |
2017 |
| language |
English |
| container_title |
Symmetry, Integrability and Geometry: Methods and Applications |
| publisher |
Інститут математики НАН України |
| format |
Article |
| description |
Let p be any point in the moduli space of genus-two curves M2 and K its field of moduli. We provide a universal equation of a genus-two curve Cα,β defined over K(α,β), corresponding to p, where α and β satisfy a quadratic α²+bβ²=c such that b and c are given in terms of ratios of Siegel modular forms. The curve Cα,β is defined over the field of moduli K if and only if the quadratic has a K-rational point (α,β). We discover some interesting symmetries of the Weierstrass equation of Cα,β. This extends previous work of Mestre and others.
|
| issn |
1815-0659 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/149268 |
| citation_txt |
A Universal Genus-Two Curve from Siegel Modular Forms / A. Malmendier, T. Shaska // Symmetry, Integrability and Geometry: Methods and Applications. — 2017. — Т. 13. — Бібліогр.: 19 назв. — англ. |
| work_keys_str_mv |
AT malmendiera auniversalgenustwocurvefromsiegelmodularforms AT shaskat auniversalgenustwocurvefromsiegelmodularforms AT malmendiera universalgenustwocurvefromsiegelmodularforms AT shaskat universalgenustwocurvefromsiegelmodularforms |
| first_indexed |
2025-12-07T16:29:09Z |
| last_indexed |
2025-12-07T16:29:09Z |
| _version_ |
1850867658878091264 |