English

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 (1,t)(1,t)-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

R2 v1 2026-06-23T10:01:46.975Z