Universal abelian variety and Siegel modular forms
Algebraic Geometry
2019-10-15 v2 Number Theory
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 its certain compactifications, 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.
Cite
@article{arxiv.1810.04834,
title = {Universal abelian variety and Siegel modular forms},
author = {Shouhei Ma},
journal= {arXiv preprint arXiv:1810.04834},
year = {2019}
}