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Compact quotients with positive algebraic dimensions of large domains in a complex projective 3-space
Masahide KATO
Source: J. Math. Soc. Japan Volume 62, Number 4
(2010), 1317-1371.
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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Permanent link to this document: http://projecteuclid.org/euclid.jmsj/1288703107
Digital Object Identifier: doi:10.2969/jmsj/06241317
Zentralblatt MATH identifier: 05835145
Mathematical Reviews number (MathSciNet): MR2761899
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