Cohomological characterizations of projective spaces and hyperquadrics

Abstract

We confirm Beauville's conjecture that claims that if the p-th exterior power of the tangent bundle of a smooth projective variety contains the p-th power of an ample line bundle, then the variety is either the projective space or the p-dimensional quadric hypersurface.

Added Lemma 2.8 and slightly changed proof of Lemma 6.2 to make them apply for torsion-free sheaves and not only to vector bundles

References in corpus (1)

• On covering and quasi-unsplit families of rational curves

Cited by in corpus (3)

• Characterizations of Projective Spaces and Hyperquadrics via Positivity Properties of the Tangent Bundle
• Characterizations of projective spaces and hyperquadrics
• Identifying quadric bundle structures on complex projective varieties