A Universal Genus-Two Curve from Siegel Modular Forms

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2017
• Main Authors: Malmendier, A., Shaska, T.
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2017
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/149268
• 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.

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...