Universal abelian variety and Siegel modular forms

Ma, Shouhei

doi:10.2140/ant.2021.15.2089

Download this article
	For screen
	For printing

Recent Issues

The Journal

About the journal

Ethics and policies

Peer-review process

Submission guidelines

ISSN 1944-7833 (online)

ISSN 1937-0652 (print)

Author index

To appear

Other MSP journals

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.

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