Holomorphic geometric structures on Kähler–Einstein manifolds

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Holomorphic geometric structures on Kähler–Einstein manifolds

McKay, Benjamin
Date: 2016-08-12
Copyright: © 2016, Springer-Verlag Berlin Heidelberg. This is a post-peer-review, pre-copyedit version of an article published in manuscripta mathematica. The final authenticated version is available online at: https://doi.org/10.1007/s00229-016-0873-8
Citation: McKay, B. (2017) 'Holomorphic geometric structures on Kähler–Einstein manifolds', manuscripta mathematica, 153(1), pp. 1-34. doi:10.1007/s00229-016-0873-8
Published Version: 10.1007/s00229-016-0873-8

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.

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