Complex structures on products of circle bundles over complex manifolds [Structures complexes sur les produits de fibrés en cercles au dessus des variétés complexes]

摘要

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 X_i:=G_i/P_i, i=1,2, where the G_i are complex semisimple linear Lie groups and the P_i?G_i are parabolic subgroups. The resulting manifold S is non-symplectic and hence non-K?hlerian. We show that the group Pic0(S) of topologically trivial holomorphic line bundles on S is isomorphic to C.