Normal Algebraic Surfaces with Trivial Bicanonical Divisor

Abstract

LetSbe a rational projective algebraic surface, with at worst quotient singular points but with no rational double singular points, such thatIKS∼0 for some minimal positive integerI. IfI=2, we prove that the fundamental group π1(S−SingS) is soluble of order ≤256 (Theorem 1). IfI≥3 orShas at worst rational double singular points, then, in general, π1(S−SingS) is not finite (remark to Theorem 1).