On Schoen surfaces

Abstract

We give a new construction of the irregular surfaces of general type with $p_g=5,\chi =2,K^2=8$,recently discovered by C. Schoen in [24]. Our approach proves that, if $S$ is a general Schoen surface, its canonical map is a finite morphism of degree 2 onto a canonical surface with invariants $p_g=5,\chi =6,K^2=8$, a complete intersection of a quadric and a quartic hypersurface in ${\mathbb{P}}^4$, with 40 even nodes.