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

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.