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October, 2010 Compact quotients with positive algebraic dimensions of large domains in a complex projective 3-space
Masahide KATO
J. Math. Soc. Japan 62(4): 1317-1371 (October, 2010). DOI: 10.2969/jmsj/06241317

Abstract

A domain in a complex 3-dimensional projective space is said to be large, if the domain contains a line, i.e., a projective linear subspace of dimension one. We study compact complex 3-manifolds defined as non-singular quotients of large domains. Any holomorphic automorphism of a large domain becomes an element of the projective linear transformations. In the first half, we study the limit sets of properly discontinuous groups acting on large domains. In the second half, we determine all compact complex 3-manifolds with positive algebraic dimensions which are quotients of large domains.

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Masahide KATO. "Compact quotients with positive algebraic dimensions of large domains in a complex projective 3-space." J. Math. Soc. Japan 62 (4) 1317 - 1371, October, 2010. https://doi.org/10.2969/jmsj/06241317

Information

Published: October, 2010
First available in Project Euclid: 2 November 2010

zbMATH: 1211.32014
MathSciNet: MR2761899
Digital Object Identifier: 10.2969/jmsj/06241317

Subjects:
Primary: 32J17
Secondary: 32D15 , 32M05 , 32Q57

Keywords: algebraic dimension , compact non-Kahler manifold , projective structure

Rights: Copyright © 2010 Mathematical Society of Japan

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Vol.62 • No. 4 • October, 2010
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