Fundamental groups of compact complete locally affine complex surfaces

Jay Paul Fillmore and John Herman Scheuneman

Vol. 44 (1973), No. 2, 487–496

DOI: 10.2140/pjm.1973.44.487

Abstract

The fundamental group of a compact complete locally affine complex manifold of two complex dimensions is a solvable group which is a finite cyclic extension of a nilpotent or abelian group. Such a manifold has vanishing Euler characteristic and is finitely covered by a nilmanifold. A description of these manifolds and their fundamental groups is obtained in the course of the proofs of these facts.

Mathematical Subject Classification 2000

Primary: 32M05

Secondary: 20F05

Milestones

Received: 13 September 1971

Published: 1 February 1973