Symmetries of holomorphic geometric structures on tori
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Published Version
Date
2016
Authors
Dumitrescu, Sorin
McKay, Benjamin
Journal Title
Journal ISSN
Volume Title
Publisher
De Gruyter Open
Published Version
Abstract
We 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.
Description
Keywords
Locally homogeneous structures , Complex tori
Citation
Dumitrescu, S. and McKay, B. (2016). 'Symmetries of holomorphic geometric structures on tori', Complex Manifolds, 3(1), pp. 1-15. doi: 10.1515/coma-2016-0001