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.
Fallucca, F., Pignatelli, R. (2024). Smooth k-double covers of the plane of geometric genus 3. RENDICONTI DI MATEMATICA E DELLE SUE APPLICAZIONI, 45(3), 153-180.
Smooth k-double covers of the plane of geometric genus 3
Fallucca, F;
2024
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.
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