COMPLEX-ANALYTIC INTERMEDIATE HYPERBOLICITY, AND FINITENESS PROPERTIES

Antoine Etesse (1)

1 I2M - Institut de Mathématiques de Marseille

Motivated by the finiteness of the set of automorphisms Aut(X) of a projective manifold X, and by Kobayashi-Ochiai's conjecture that a projective manifold dim(X)-analytically hyperbolic (also known as strongly measure hyperbolic) should be of general type, we investigate the finiteness properties of Aut(X) for a complex manifold satisfying a (pseudo-) intermediate hyperbolicity property. We first show that a complex manifold X which is (dim(X) − 1)-analytically hyperbolic has indeed finite automorphisms group. We then obtain a similar statement for a pseudo-(dim(X) − 1)-analytically hyperbolic, strongly measure hyperbolic projective manifold X, under an additional hypothesis on the size of the degeneracy set. Some of the properties used during the proofs lead us to introduce a notion of intermediate Picard hyperbolicity, which we last discuss.

Mots clés: Positivity; Moduli spaces of maps; 32Q45 Hyperbolicity; 32Q05 Negative curvature complex manifolds

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

Antoine Etesse. COMPLEX-ANALYTIC INTERMEDIATE HYPERBOLICITY, AND FINITENESS PROPERTIES. 2020. ⟨hal-03021078⟩