Universal abelian variety and Siegel modular forms

Ma, Shouhei

doi:10.2140/ant.2021.15.2089

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Universal abelian variety and Siegel modular forms

Shouhei Ma

Vol. 15 (2021), No. 8, 2089–2122

DOI: 10.2140/ant.2021.15.2089

Abstract

We prove that the ring of Siegel modular forms of weight divisible by $g + n + 1$ is isomorphic to the ring of (log) pluricanonical forms on the $n$ -fold Kuga family of abelian varieties and certain compactifications of it, for every arithmetic group for a symplectic form of rank $2 g > 2$ . We also give applications to the Kodaira dimension of the Kuga variety. In most cases, the Kuga variety has canonical singularities.

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Keywords

Siegel modular forms, Kuga family, toroidal compactification, Kodaira dimension

Mathematical Subject Classification

Primary: 11F46, 14K10

Milestones

Received: 13 November 2020

Accepted: 2 March 2021

Published: 10 November 2021

Authors

Shouhei Ma
Department of Mathematics Tokyo Institute of Technology Tokyo Japan

Vol. 15, No. 8, 2021