Dolbeault cohomology of compact complex homogeneous manifolds

Ramani, Vimala ; Sankaran, Parameswaran (1999) Dolbeault cohomology of compact complex homogeneous manifolds Proceedings of the Indian Academy of Sciences - Mathematical Sciences, 109 (1). pp. 11-21. ISSN 0253-4142

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We show that if M is the total space of a holomorphic bundle with base space a simply connected homogeneous projective variety and fibre and structure group a compact complex torus, then the identity component of the automorphism group of M acts trivially on the Dolbeault cohomology ofM. We consider a class of compact complex homogeneous spaces W, which we call generalized Hopf manifolds, which are diffeomorphic to S1×K/L where K is a compact connected simple Lie group andL is the semisimple part of the centralizer of a one dimensional torus in K. We compute the Dolbeault cohomology of W. We compute the Picard group of any generalized Hopf manifold and show that every line bundle over a generalized Hopf manifold arises from a representation of its fundamental group.

Item Type:Article
Source:Copyright of this article belongs to Indian Academy of Sciences.
Keywords:Dolbeault Cohomology; Complex Homogeneous Manifolds; Generalized Hopf Manifolds; Automorphism Groups; Picard Group
ID Code:57695
Deposited On:29 Aug 2011 08:23
Last Modified:18 May 2016 09:00

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