Subvarieties of quotients of bounded symmetric domains

TL;DR

This paper introduces a new criterion for complex hyperbolicity of quotients of bounded symmetric domains, with applications to moduli spaces of curves and abelian varieties, establishing conditions for subvarieties to be of general type.

Contribution

It provides a novel criterion for hyperbolicity and general type conditions in quotients of bounded symmetric domains, with specific applications to moduli spaces.

Findings

Criteria for subvarieties to be of general type

Conditions for p-measure hyperbolicity

Effective levels for moduli spaces of curves

Abstract

We present a new criterion for the complex hyperbolicity of a non-compact quotient X of a bounded symmetric domain. For each p $\ge$ 1, this criterion gives a precise condition under which the subvarieties V $\subset$ X with dim V $\ge$ p are of general type, and X is p-measure hyperbolic. Then, we give several applications related to ball quotients, or to the Siegel moduli space of principally polarized abelian varieties. For example, we determine effective levels l for which the moduli spaces of genus g curves with l-level structures are of general type.