The orbifold fundamental group of Persson-Noether-Horikawa surfaces

Abstract

The Noether-Horikawa surfaces are the minimal surfaces S with K^2=2p_g-4. For 8 | K^2 they belong to two families of respective type C and N (connected, resp. non connected branch locus for the canonical map). For 16 | K^2 the two types are homeomorphic. Ulf Persson constructed surfaces of type N with a maximally singular canonical model X, whose topology encodes information on the differentiable structure of S. A similar analysis was done by the first author for type C. In this paper we study the genus 2 fibration on X and, in particular, our main result is (X^# being the nonsingular locus of X) π_1(X^#)= Z_4 x Z_4 if 8 | K^2 but 16 does not | K^2 π_1(X^#)= Z_4 x Z_2 if 16 | K^2.