Holomorphic geometric structures on Kähler–Einstein manifolds

Benjamin McKay

doi:10.1007/s00229-016-0873-8

Holomorphic geometric structures on Kähler–Einstein manifolds

Benjamin McKay

School of Mathematical Sciences

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

Abstract

We prove that the compact Kähler manifolds with c₁≥ 0 that admit holomorphic parabolic geometries are the flat bundles of rational homogeneous varieties over complex tori. We also prove that the compact Kähler manifolds with c₁≥ 0 that admit holomorphic cominiscule geometries are the locally Hermitian symmetric varieties.

Original language	English
Pages (from-to)	1-34
Number of pages	34
Journal	Manuscripta Mathematica
Volume	153
Issue number	1-2
DOIs	https://doi.org/10.1007/s00229-016-0873-8
Publication status	Published - 1 May 2017

Keywords

53C15
53C55
53C56

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10.1007/s00229-016-0873-8

https://hdl.handle.net/10468/6492Licence: CC BY-NC-ND

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title = "Holomorphic geometric structures on K{\"a}hler–Einstein manifolds",

abstract = "We prove that the compact K{\"a}hler manifolds with c1≥ 0 that admit holomorphic parabolic geometries are the flat bundles of rational homogeneous varieties over complex tori. We also prove that the compact K{\"a}hler manifolds with c1≥ 0 that admit holomorphic cominiscule geometries are the locally Hermitian symmetric varieties.",

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AB - We prove that the compact Kähler manifolds with c1≥ 0 that admit holomorphic parabolic geometries are the flat bundles of rational homogeneous varieties over complex tori. We also prove that the compact Kähler manifolds with c1≥ 0 that admit holomorphic cominiscule geometries are the locally Hermitian symmetric varieties.

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KW - 53C55

KW - 53C56

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Holomorphic geometric structures on Kähler–Einstein manifolds

Abstract

Keywords

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