Holomorphic Cartan geometries, Calabi-Yau manifolds and rational curves

Biswas, Indranil ; McKay, Benjamin (2010) Holomorphic Cartan geometries, Calabi-Yau manifolds and rational curves Differential Geometry and its Applications, 28 (1). pp. 102-106. ISSN 0926-2245

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Official URL: http://linkinghub.elsevier.com/retrieve/pii/S09262...

Related URL: http://dx.doi.org/10.1016/j.difgeo.2009.09.003

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 Kahler manifolds. We also classify all holomorphic Cartan geometries on rationally connected complex projective manifolds.

Item Type:Article
Source:Copyright of this article belongs to Elsevier Science.
Keywords:Cartan geometry; Holomorphic connection; Calabi-Yau manifold; Rational curve
ID Code:3491
Deposited On:12 Oct 2010 04:29
Last Modified:27 Jan 2011 05:55

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