Antisymmetric paramodular forms of weight 3

V. A. Gritsenko   ; H. Wang

Sbornik. Mathematics, Tome 210 (2019) no. 12, pp. 1702-1723

Résumé

The problem of the construction of antisymmetric paramodular forms of canonical weight 3 has been open since 1996. Any cusp form of this type determines a canonical differential form on any smooth compactification of the moduli space of Kummer surfaces associated to $(1,t)$-polarised abelian surfaces. In this paper, we construct the first infinite family of antisymmetric paramodular forms of weight $3$ as automorphic Borcherds products whose first Fourier-Jacobi coefficient is a theta block. Bibliography: 32 titles.

Détail

Keywords: Siegel modular forms, automorphic Borcherds products, theta functions and Jacobi forms, moduli space of abelian and Kummer surfaces, affine Lie algebras and hyperbolic Lie algebras.

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