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.
@article{bwmeta1.element.doi-10_1515_coma-2016-0001,
author = {Sorin Dumitrescu and Benjamin McKay},
title = {Symmetries of holomorphic geometric structures on tori},
journal = {Complex Manifolds},
volume = {3},
year = {2016},
zbl = {1357.32017},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_1515_coma-2016-0001}
}
Sorin Dumitrescu; Benjamin McKay. Symmetries of holomorphic geometric structures on tori. Complex Manifolds, Tome 3 (2016) . http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_1515_coma-2016-0001/