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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Official URL: http://www.ias.ac.in/j_archive/mathsci/109/1/11-21...
Related URL: http://dx.doi.org/10.1007/BF02837763
Abstract
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 |
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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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