Antisymmetric paramodular forms of weight 3
Number Theory
2019-06-25 v1 Algebraic Geometry
Abstract
The problem on the construction of antisymmetric paramodular forms of canonical weight 3 was open since 1998. Any cusp form of this type determines a canonical differential form on any smooth compactification of the moduli space of Kummer surfaces associated to -polarised abelian surfaces. In this paper, we construct the first infinite family of antisymmetric paramodular forms of weight 3 as Borcherds products whose first Fourier-Jacobi coefficient is a theta block.
Keywords
Cite
@article{arxiv.1906.09869,
title = {Antisymmetric paramodular forms of weight 3},
author = {Valery Gritsenko and Haowu Wang},
journal= {arXiv preprint arXiv:1906.09869},
year = {2019}
}
Comments
accepted for publication in Sbornik: Mathematics