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. The last two are irreducible components of the moduli space of minimal surfaces of general type with $K^{2}=8$, $p_{g}=4$. These families hit three different topological types.