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 (2)

• Symplectic singularities
• On covering and quasi-unsplit families of rational curves

Cited by in corpus (18)

• Codimension one foliations with numerically trivial canonical class on singular spaces
• Bigness of the tangent bundle of del Pezzo surfaces and $D$-simplicity
• Codimension one Fano distributions on Fano manifolds
• Characterization of projective spaces and ${\mathbb{P}}^r$-bundles as ample divisors
• On codimension 1 del Pezzo foliations on varieties with mild singularities
• On Fano foliations 2
• Algebraic fibre spaces with strictly nef relative anti-log canonical divisor
• On pseudoeffective thresholds and cohomology of twisted symmetric tensor fields on irreducible Hermitian symmetric spaces
• Del Pezzo foliations with log canonical singularities
• Fano manifolds and stability of tangent bundles
• Characterizations of Projective Spaces and Hyperquadrics via Positivity Properties of the Tangent Bundle
• Uniformisation of higher-dimensional minimal varieties
• A decomposition theorem for $\mathbb{Q}$-Fano Kähler-Einstein varieties
• Second Chern class of Fano manifolds and anti-canonical geometry
• Characterizations of projective spaces and hyperquadrics
• Identifying quadric bundle structures on complex projective varieties
• Strictly nef vector bundles and characterizations of ${\mathbb{P}}^n$
• On projective varieties with strictly nef tangent bundles