Holomorphic Cartan geometries on complex tori

Indranil Biswas (1) , Sorin Dumitrescu (2)

1 TIFR - Tata Institute for Fundamental Research
2 LJAD - Laboratoire Jean Alexandre Dieudonné

In [DM] it was asked whether all flat holomorphic Cartan geometries (G,H) on a complex torus are translation invariant. We answer this affimatively under the assumption that the complex Lie group G is affine. More precisely, we show that every holomorphic Cartan geometry of type (G,H), with G a complex affine Lie group, on any complex torus is translation invariant.

Mots clés: complex torus; holomorphic Cartan geometries; translation invariance

Domaines: Mathématiques [math]

Indranil Biswas, Sorin Dumitrescu. Holomorphic Cartan geometries on complex tori. Comptes Rendus. Mathématique, 2018, 356, pp.316-321. ⟨hal-01617650⟩