Analytic Geometry
Stability and holomorphic connections on vector bundles over LVMB manifolds
Comptes Rendus. Mathématique, Volume 358 (2020) no. 2, pp. 151-157.

We characterize all LVMB manifolds X such that the holomorphic tangent bundle TX is spanned at the generic point by a family of global holomorphic vector fields, each of them having non-empty zero locus. We deduce that holomorphic connections on semi-stable holomorphic vector bundles over LVMB manifolds with this previous property are always flat.

Nous caractérisons les variétés LVMB qui ont la propriété de positivité 𝒫 suivante : le fibré tangent holomorphe est engendré au point générique par une famille de champs de vecteurs holomorphes (globalement définis) {v i }, tel que chaque v i s’annule en au moins un point de X. Nous en déduisons que, sur les variétés LVMB avec la propriété 𝒫, les connexions holomorphes sur les fibrés vectoriels holomorphes semi-stables sont nécessairement plates.

Received:
Accepted:
Published online:
DOI: 10.5802/crmath.24
Classification: 32Q26,  32M12,  53B05
Biswas, Indranil 1; Dumitrescu, Sorin 2; Meersseman, Laurent 3

1 School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai 400005, India
2 Université Côte d’Azur, CNRS, LJAD
3 Laboratoire Angevin de Recherche en Mathématiques, Université d’Angers, Université de Bretagne-Loire F-49045 Angers Cedex, France
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Biswas, Indranil; Dumitrescu, Sorin; Meersseman, Laurent. Stability and holomorphic connections on vector bundles over LVMB manifolds. Comptes Rendus. Mathématique, Volume 358 (2020) no. 2, pp. 151-157. doi : 10.5802/crmath.24. http://www.numdam.org/articles/10.5802/crmath.24/

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