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.

Smooth k-double Covers of the Plane of Geometric Genus 3 / Fallucca, F.; Pignatelli, R.. - In: RENDICONTI DI MATEMATICA E DELLE SUE APPLICAZIONI. - ISSN 1120-7183. - STAMPA. - 2024, 45:3(2024), pp. 153-180.

Smooth k-double Covers of the Plane of Geometric Genus 3

Fallucca F.;Pignatelli R.
2024-01-01

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.
2024
3
Fallucca, F.; Pignatelli, R.
Smooth k-double Covers of the Plane of Geometric Genus 3 / Fallucca, F.; Pignatelli, R.. - In: RENDICONTI DI MATEMATICA E DELLE SUE APPLICAZIONI. - ISSN 1120-7183. - STAMPA. - 2024, 45:3(2024), pp. 153-180.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11572/409710
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