Cohomological characterizations of projective spaces and hyperquadrics.

Abstract:

In 1979, S. Mori characterized projective spaces as the only manifolds having
ample tangent bundles. Since then, characterizations of projective  
spaces in terms of positivity properties of the tangent bundle have  
been subject of much investigation.

In this talk I will present a recent characterization of projective spaces and
hyperquadrics that had been conjectured by Beauville. Namely, if the  
p-th exterior power of the tangent bundle of a complex manifold $X$  
contains the p-th power of an ample line bundle, then $X$ is either  
the projective space or the p-dimensional hyperquadric.

This is a joint work with St\'ephane Druel and S\'andor Kov\'acs.