Journal of the Mathematical Society of Japan
- J. Math. Soc. Japan
- Volume 62, Number 4 (2010), 1317-1371.
Compact quotients with positive algebraic dimensions of large domains in a complex projective 3-space
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.
J. Math. Soc. Japan Volume 62, Number 4 (2010), 1317-1371.
First available in Project Euclid: 2 November 2010
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
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
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. http://projecteuclid.org/euclid.jmsj/1288703107.