English

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.

Keywords

Cite

@article{arxiv.1810.04834,
  title  = {Universal abelian variety and Siegel modular forms},
  author = {Shouhei Ma},
  journal= {arXiv preprint arXiv:1810.04834},
  year   = {2019}
}
R2 v1 2026-06-23T04:35:44.639Z