On subvarieties of singular quotients of bounded domains

Benoit Cadorel (1) , Simone Diverio (2) , Henri Guenancia (1, 3)

1 IMT - Institut de Mathématiques de Toulouse UMR5219
2 Sapienza University of Rome - Dipartimento di Matematica "Guido Castelnuovo" [Roma I]
3 CNRS - Centre National de la Recherche Scientifique

Let $X$ be a quotient of a bounded domain in $\mathbb C^n$. Under suitable assumptions, we prove that every subvariety of $X$ not included in the branch locus of the quotient map is of log general type in some orbifold sense, generalizing Boucksom and Diverio's result in the \'etale and compact case. Finally, in the case where $X$ is compact, we give a sufficient condition under which there exists a proper analytic subset of $X$ containing all entire curves and all subvarieties not of general type (meant this time in in the usual sense as opposed to the orbifold sense).

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

Benoit Cadorel, Simone Diverio, Henri Guenancia. On subvarieties of singular quotients of bounded domains. 2020. ⟨hal-02134317v1⟩