Subvarieties of quotients of bounded symmetric domains

الأصل · EN

We present a new criterion for the complex hyperbolicity of a non-compact quotient X of a bounded symmetric domain. For each p ≥ 1, this criterion gives a precise condition under which the subvarieties V ⊂ X with dim V ≥ 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.