Cohomological characterizations of projective spaces and hyperquadrics

TL;DR

This paper proves Beauville's conjecture that certain conditions on the tangent bundle of a smooth projective variety imply it is either a projective space or a hyperquadric, advancing the classification of such varieties.

Contribution

It confirms Beauville's conjecture linking tangent bundle properties to the classification of projective varieties, specifically characterizing projective spaces and hyperquadrics.

Findings

Confirmed Beauville's conjecture for smooth projective varieties

Characterized varieties with specific tangent bundle properties

Extended understanding of the structure of projective varieties

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.