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arXiv · 1009.5801

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

Indranil Biswas·Benjamin McKay
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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.

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Indranil Biswas, Benjamin McKay. 2010-09-29. Holomorphic Cartan geometries, Calabi--Yau manifolds and rational curves. https://doi.org/10.1016/j.difgeo.2009.09.003

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