Holomorphic Cartan geometries, Calabi-Yau manifolds and rational curves

Indranil Biswas; Benjamin McKay

doi:10.1016/j.difgeo.2009.09.003

Holomorphic Cartan geometries, Calabi-Yau manifolds and rational curves

Indranil Biswas
, Benjamin McKay

School of Mathematical Sciences

Tata Institute of Fundamental Research

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	102-106
Number of pages	5
Journal	Differential Geometry and its Application
Volume	28
Issue number	1
DOIs	https://doi.org/10.1016/j.difgeo.2009.09.003
Publication status	Published - 2010

Keywords

Calabi-Yau manifold
Cartan geometry
Holomorphic connection
Rational curve

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10.1016/j.difgeo.2009.09.003

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title = "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 K{\"a}hler manifolds. We also classify all holomorphic Cartan geometries on rationally connected complex projective manifolds.",

keywords = "Calabi-Yau manifold, Cartan geometry, Holomorphic connection, Rational curve",

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AU - Biswas, Indranil

AU - McKay, Benjamin

PY - 2010

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N2 - 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.

AB - 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.

KW - Calabi-Yau manifold

KW - Cartan geometry

KW - Holomorphic connection

KW - Rational curve

UR - https://www.scopus.com/pages/publications/73249138364

U2 - 10.1016/j.difgeo.2009.09.003

DO - 10.1016/j.difgeo.2009.09.003

M3 - Article

AN - SCOPUS:73249138364

SN - 0926-2245

VL - 28

SP - 102

EP - 106

JO - Differential Geometry and its Application

JF - Differential Geometry and its Application

IS - 1

ER -

Holomorphic Cartan geometries, Calabi-Yau manifolds and rational curves

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Keywords

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