Surfaces on the Severi line

Abstract

Let S be a minimal complex surface of general type and of maximal Albanese dimension; by the Severi inequality one has $K_S^2\ge 4\chi ({\mathcal{O}}_S)$. We prove that the equality $K_S^2=4\chi ({\mathcal{O}}_S)$ holds if and only if $q(S):=h^1({\mathcal{O}}_S)=2$ and the canonical model of $S$ is a double cover of the Albanese surface branched on an ample divisor with at most negligible singularities.

13 pages