Comptes Rendus
Algebraic Geometry/Analytic Geometry
Complex structures on products of circle bundles over complex manifolds
[Structures complexes sur les produits de fibrés en cercles au dessus des variétés complexes]
Comptes Rendus. Mathématique, Volume 349 (2011) no. 7-8, pp. 437-439.

Dans ce Note, on propose une construction de structures complexes sur le produit de deux fibré en cercles associés aux fibrés en droites, amples, négatifs sur des variétés drapeaux Xi=Gi/Pi, i=1,2, où les Gi sont des groupes de Lie linéaires connexes, complexes, semi-simples et les PiGi sont des sous-groupes paraboliques. La variété construite S nʼest pas symplectique et donc nʼest pas kählérienne. On démontre que le groupe Pic0(S) des fibrés en droites holomorphes topologiquement triviaux est isomorphe aux nombres complexes C.

We propose, in this Note, a construction of complex structures on the product of two circle bundles associated to negative ample line bundles over flag varieties Xi:=Gi/Pi, i=1,2, where the Gi are complex semisimple linear Lie groups and the PiGi are parabolic subgroups. The resulting manifold S is non-symplectic and hence non-Kählerian. We show that the group Pic0(S) of topologically trivial holomorphic line bundles on S is isomorphic to C.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2011.02.016

Parameswaran Sankaran 1 ; Ajay Singh Thakur 1

1 The Institute of Mathematical Sciences, CIT Campus, Taramani, Chennai 600113, India
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Parameswaran Sankaran; Ajay Singh Thakur. Complex structures on products of circle bundles over complex manifolds. Comptes Rendus. Mathématique, Volume 349 (2011) no. 7-8, pp. 437-439. doi : 10.1016/j.crma.2011.02.016. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2011.02.016/

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