Vol. 15, No. 8, 2021

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Universal abelian variety and Siegel modular forms

Shouhei Ma

Vol. 15 (2021), No. 8, 2089–2122
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 2g > 2. We also give applications to the Kodaira dimension of the Kuga variety. In most cases, the Kuga variety has canonical singularities.

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