Smooth k-double covers of the plane of geometric genus 3
Algebraic Geometry
2023-08-01 v2
Abstract
In this work we classify all smooth surfaces with geometric genus equal to three and an action of a group G isomorphic to (Z/2)^k such that the quotient is a plane. We find 11 families. We compute the canonical map of all of them, finding in particular a family of surfaces with canonical map of degree 16 that we could not find in the literature. We discuss the quotients by all subgroups of G finding several K3 surfaces with symplectic involutions. In particular we show that six families are families of triple K3 burgers in the sense of Laterveer.
Keywords
Cite
@article{arxiv.2305.04545,
title = {Smooth k-double covers of the plane of geometric genus 3},
author = {Federico Fallucca and Roberto Pignatelli},
journal= {arXiv preprint arXiv:2305.04545},
year = {2023}
}
Comments
30 pages. v2: added a comment on the dependence of the three involutions that determine the structure of triple K3 burgers. Final version to appear on Rend. Mat. Appl. (7)