Symmetries of holomorphic geometric structures on tori-Reference-Cited by-同舟云学术

Symmetries of holomorphic geometric structures on tori

Published:2016-01-21 Issue:1 Volume:3 Page:
ISSN:2300-7443
Container-title:Complex Manifolds
language:
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Author:

Dumitrescu Sorin¹,McKay Benjamin²

Affiliation:

1. 1Universit´e Cˆote d’Azur, Universit´e Nice Sophia Antipolis, UMR CNRS 7351, Laboratoire J.-A. Dieudonn´e, Parc Valrose, 06108 NICE Cedex 02, France

2. 2University College Cork, Cork, Ireland

Abstract

AbstractWe prove that any holomorphic locally homogeneous geometric structure on a complex torus of dimension two, modelled on a complex homogeneous surface, is translation invariant. We conjecture that this result is true in any dimension. In higher dimension, we prove it for G nilpotent. We also prove that for any given complex algebraic homogeneous space (X, G), the translation invariant (X, G)-structures on tori form a union of connected components in the deformation space of (X, G)-structures.

Publisher

Walter de Gruyter GmbH

Subject

Geometry and Topology

Link

https://www.degruyter.com/downloadpdf/journals/coma/open-issue/article-10.1515-coma-2016-0001/article-10.1515-coma-2016-0001.xml

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