Journal of the Mathematical Society of Japan

Compact quotients with positive algebraic dimensions of large domains in a complex projective 3-space

Masahide KATO

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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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J. Math. Soc. Japan Volume 62, Number 4 (2010), 1317-1371.

First available in Project Euclid: 2 November 2010

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Mathematical Reviews number (MathSciNet)

Primary: 32J17: Compact $3$-folds
Secondary: 32M05: Complex Lie groups, automorphism groups acting on complex spaces [See also 22E10] 32Q57: Classification theorems 32D15: Continuation of analytic objects

compact non-Kahler manifold projective structure algebraic dimension


KATO, Masahide. Compact quotients with positive algebraic dimensions of large domains in a complex projective 3-space. J. Math. Soc. Japan 62 (2010), no. 4, 1317--1371. doi:10.2969/jmsj/06241317.

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