New surfaces with $K^2=7$ and $p_g=q\le 2$

Abstract

We construct smooth minimal complex surfaces of general type with $K^2=7$ and: $p_g=q=2,$ Albanese map of degree $2$ onto a $(1,2)$-polarized abelian surface; $p_g=q=1$ as a double cover of a quartic Kummer surface; $p_g=q=0$ as a double cover of a numerical Campedelli surface with $5$ nodes.

arXiv commentExposition improved according to Referees' comments. Final version

References in corpus (1)

• On the computation of singular plane curves and quartic surfaces