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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| Видавець: | Інститут математики НАН України |
|---|---|
| Дата: | 2017 |
| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2017
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| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/149268 |
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| Цитувати: | 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. |
Репозиторії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
irk-123456789-149268 |
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| record_format |
dspace |
| spelling |
irk-123456789-1492682019-02-20T01:23:42Z A Universal Genus-Two Curve from Siegel Modular Forms Malmendier, A. Shaska, T. 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. 2017 Article 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 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| 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. |
| format |
Article |
| author |
Malmendier, A. Shaska, T. |
| spellingShingle |
Malmendier, A. Shaska, T. A Universal Genus-Two Curve from Siegel Modular Forms Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Malmendier, A. Shaska, T. |
| author_sort |
Malmendier, A. |
| title |
A Universal Genus-Two Curve from Siegel Modular Forms |
| 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 |
| publisher |
Інститут математики НАН України |
| publishDate |
2017 |
| url |
http://dspace.nbuv.gov.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. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
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2023-05-20T17:31:43Z |
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2023-05-20T17:31:43Z |
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