Subvarieties of quotients of bounded symmetric domains

DOI10.1007/S00208-021-02295-3arXiv1809.10978MaRDI QIDQ6307449

Benoît Cadorel

Publication date: 28 September 2018

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.

Mathematics Subject Classification ID

Hermitian symmetric spaces, bounded symmetric domains, Jordan algebras (complex-analytic aspects) (32M15) Hyperbolic and Kobayashi hyperbolic manifolds (32Q45)

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