Normal algebraic surfaces with trivial bicanonical divisor

Abstract

Let S be a rational projective algebraic surface, with at worst quotient singular points but with no rational double singular points, such that IKS ∼ 0 for some minimal positive integer I. If I = 2, we prove that the fundamental group π1(S -Sing S) is soluble of order ≤ 256 (Theorem 1). If I ≥ 3 or S has at worst rational double singular points, then, in general, π1(S - Sing S) is not finite (remark to Theorem 1). © 1996 Academic Press, Inc.