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...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Date: | 2017 |
| Main Authors: | , |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2017
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/149268 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | 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. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862697094136987648 |
|---|---|
| author | Malmendier, A. Shaska, T. |
| author_facet | Malmendier, A. Shaska, T. |
| 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. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| 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.
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| first_indexed | 2025-12-07T16:29:09Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-149268 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T16:29:09Z |
| publishDate | 2017 |
| publisher | Інститут математики НАН України |
| 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 |
| spellingShingle | A Universal Genus-Two Curve from Siegel Modular Forms Malmendier, A. Shaska, T. |
| title | 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_short | A Universal Genus-Two Curve from Siegel Modular Forms |
| title_sort | universal genus-two curve from siegel modular forms |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/149268 |
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