AMPLENESS OF SCHUR POWERS OF COTANGENT BUNDLES AND k-HYPERBOLICITY

Antoine Etesse (1)

1 I2M - Institut de Mathématiques de Marseille

In this paper, we study a variation of a conjecture of Debarre on positivity of cotangent bundles of complete intersections. We establish the ampleness of Schur powers of cotangent bundles of generic complete intersections in projective manifolds, with high enough explicit codimension and multi-degrees. Our approach is naturally formulated in terms of flag bundles and allows one to reach the optimal codimension. On complex manifolds, this ampleness property implies intermediate hyperbolic properties. We give a natural application of our main result in this context.

Mots clés: Ampleness; Cotangent bundle; Schur power; Hyperbolicity of projective varieties; Ampleness

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

Antoine Etesse. AMPLENESS OF SCHUR POWERS OF COTANGENT BUNDLES AND k-HYPERBOLICITY. 2021. ⟨hal-02190039v2⟩