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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Borel's fixed point theorem for Kaehler manifolds and an application


Author: Andrew J. Sommese
Journal: Proc. Amer. Math. Soc. 41 (1973), 51-54
MSC: Primary 32M10; Secondary 53C30
MathSciNet review: 0322217
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Abstract: A short proof of a generalization of the Borel fixed point theorem to the case of Kaehler manifolds is given and, as an application, a short proof of Wang's theorem that compact simply connected homogeneous manifolds are projective and of the form $ G/P$, where $ G$ is a complex semisimple Lie group and $ P$ is a parabolic subgroup.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1973-0322217-0
PII: S 0002-9939(1973)0322217-0
Keywords: Transcendental algebraic geometry and Hodge theory, homogeneous manifolds, automorphism groups of complex manifolds, Kaehler manifolds
Article copyright: © Copyright 1973 American Mathematical Society