A Universal Genus-Two Curve from Siegel Modular Forms
Vernadsky National Library of Ukraine
Переглянути архів Інформація| Поле | Співвідношення | |
| Title |
A Universal Genus-Two Curve from Siegel Modular Forms
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| Creator |
Malmendier, A.
Shaska, T. |
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| 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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| Date |
2019-02-19T19:32:49Z
2019-02-19T19:32:49Z 2017 |
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| Type |
Article
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| Identifier |
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 http://dspace.nbuv.gov.ua/handle/123456789/149268 |
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| Language |
en
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| Relation |
Symmetry, Integrability and Geometry: Methods and Applications
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| Publisher |
Інститут математики НАН України
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