HYPERBOLICITY OF BASES OF LOG CALABI-YAU FAMILIES

Ya Deng (1, 2)

1 Chalmers - Department of Mathematical Sciences
2 Göteborg - Department of Mathematical Sciences

We prove that for any maximally varying, log smooth family of Calabi-Yau klt pairs, its quasi-projective base is both of log general type, and pseudo Kobayashi hyperbolic. Moreover, such a base is Brody hyperbolic if the family is effectively parametrized.

Mots clés: pseudo Kobayashi hyperbolicity; Viehweg hyperbolicity; Brody hyperbolicity; log Calabi-Yau family; Viehweg-Zuo Higgs bundles; Campana-Paun criterion; Finsler metric

Domaines: Géométrie algébrique [math.AG]; Variables complexes [math.CV]

Ya Deng. HYPERBOLICITY OF BASES OF LOG CALABI-YAU FAMILIES. 2019. ⟨hal-02266744⟩