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.
- Publication:
-
Inventiones Mathematicae
- Pub Date:
- August 2008
- DOI:
- 10.1007/s00222-008-0130-1
- arXiv:
- arXiv:0707.4310
- Bibcode:
- 2008InMat.174..233A
- Keywords:
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- Mathematics - Algebraic Geometry;
- 14M20
- E-Print:
- 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