Surfaces with K^2=8, p_g=4 and canonical involution

Abstract

In this paper we classify completely all regular minimal surfaces with K^2=8, p_g=4 whose canonical map is composed with an involution. We obtain six unirational families of respective dimensions 28,28,32,33,38,34. The last two are irreducible components of the moduli space of minimal surfaces with K^2=8, p_g=4. These families hit three different topological types.

23 pages. In this version we correct an error (which does not change the main theorem) and simplify substantially some proofs. For sake of clarity we decided to be more detailed in the case of surfaces having a genus 2 pencil