Universal abelian variety and Siegel modular forms

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.

References in corpus (2)

• Modular forms of weight 3m and elliptic modular surface
• The dimensions of spaces of Siegel cusp forms of general degree

Cited by in corpus (1)

• Mukai models and Borcherds products