Comptes Rendus
no. 3
Analytic geometry
Holomorphic Cartan geometries on complex tori
[Géométries de Cartan holomorphes sur les tores complexes]
Présenté par : Jean-Pierre Demailly
Indranil Biswas1 ; Sorin Dumitrescu2
1 School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai 400005, India
2 Université Côte d'Azur, CNRS, LJAD, France
Comptes Rendus. Mathématique, Volume 356 (2018) no. 3, pp. 316-321

In [6], it was asked whether all flat holomorphic Cartan geometries (G,H) on a complex torus are translation invariant. We answer this affirmatively 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.

Nous démontrons que, sur les tores complexes, toutes les géométries de Cartan holomorphes modelées sur (G,H), avec G groupe de Lie complexe affine, sont invariantes par translation.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2018.02.005

Indranil Biswas 1 ; Sorin Dumitrescu 2

1 School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai 400005, India
2 Université Côte d'Azur, CNRS, LJAD, France 
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Indranil Biswas; Sorin Dumitrescu. Holomorphic Cartan geometries on complex tori. Comptes Rendus. Mathématique, Volume 356 (2018) no. 3, pp. 316-321. doi: 10.1016/j.crma.2018.02.005

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