Holomorphic Cartan geometries, CalabiYau manifolds and rational curves
Abstract
We prove that if a CalabiYau manifold $M$ admits a holomorphic Cartan geometry, then $M$ is covered by a complex torus. This is done by establishing the Bogomolov inequality for semistable sheaves on compact Kähler manifolds. We also classify all holomorphic Cartan geometries on rationally connected complex projective manifolds.
 Publication:

arXiv eprints
 Pub Date:
 September 2010
 arXiv:
 arXiv:1009.5801
 Bibcode:
 2010arXiv1009.5801B
 Keywords:

 Mathematics  Algebraic Geometry;
 Mathematics  Differential Geometry;
 32Q25 (14J32 53Cxx)
 EPrint:
 7 pages