Holomorphic Cartan geometries, Calabi--Yau manifolds and rational curves

Abstract

We prove that if a Calabi--Yau 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.

arXiv comment7 pages

References in corpus (4)

• On the Differential Geometry of $G{L}_q(1|1)$
• Holomorphic Parabolic Geometries and Calabi-Yau Manifolds
• Holomorphic Cartan geometries and Calabi--Yau manifolds
• Complete complex parabolic geometries

Cited by in corpus (4)

• Holomorphic Parabolic Geometries and Calabi-Yau Manifolds
• Geometric structures modeled on smooth projective horospherical varieties of Picard number one
• Logarithmic Cartan geometry on complex manifolds
• Generalized Holomorphic Cartan geometries