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## Antisymmetric paramodular forms of weight 3

Sbornik Mathematics. 2019. Vol. 210. No. 12.
Gritsenko V., Wang H.

The problem on the construction of antisymmetric paramodular forms of canonical weight $3$ was 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 Borcherds products whose first Fourier-Jacobi coefficient is a theta block.