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

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.

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Siegel modular forms, Kuga family, toroidal compactification, Kodaira dimension
Mathematical Subject Classification
Primary: 11F46, 14K10
Received: 13 November 2020
Accepted: 2 March 2021
Published: 10 November 2021
Shouhei Ma
Department of Mathematics
Tokyo Institute of Technology