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 Mat. Sb., 2019, Volume 210, Number 12, Pages 43–66 (Mi msb9241)

Antisymmetric paramodular forms of weight 3

V. A. Gritsenkoab, H. Wanga

a Laboratoire Paul Painlevé, Université de Lille, Villeneuve d’Ascq, France
b National Research University Higher School of Economics, Moscow, Russia

Abstract: 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.

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.

 Funding Agency Grant Number Ministry of Education and Science of the Russian Federation 14.641.31.0001 Labex ANR-11- LABX-0007-01 V. A. Gritsenko was supported by the Laboratory of Mirror Symmetry, NRU HSE, RF government grant, agreement no. 14.641.31.0001. H. Wang was supported by the Laboratory of Mirror Symmetry, NRU HSE, RF government grant, agreement no. 14.641.31.0001, and by Labex CEMPI, Université de Lillé (grant no. ANR-11-LABX-0007-01).

Author to whom correspondence should be addressed

DOI: https://doi.org/10.4213/sm9241

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English version:
Sbornik: Mathematics, 2019, 210:12, 1702–1723

Bibliographic databases:

UDC: 515.178.5+512.774.5+512.818.4
MSC: 11F27, 11F30, 11F46, 11F50, 11F55, 14K25

Citation: V. A. Gritsenko, H. Wang, “Antisymmetric paramodular forms of weight 3”, Mat. Sb., 210:12 (2019), 43–66; Sb. Math., 210:12 (2019), 1702–1723

Citation in format AMSBIB
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