Symmetries of holomorphic geometric structures on tori

Sorin Dumitrescu (1) , Benjamin Mckay (2)

1 LJAD - Laboratoire Jean Alexandre Dieudonné
2 UCC - University College Cork

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

Mots clés: complex homogeneous spaces; complex tori; locally homogeneous geometric structures.

Domaines: Mathématiques [math]

Sorin Dumitrescu, Benjamin Mckay. Symmetries of holomorphic geometric structures on tori. Complex Manifolds, 2016, 3 (1), pp.1-15. ⟨hal-01205281⟩