Smooth k-double covers of the plane of geometric genus 3

2023/05/08 by Federico Fallucca, Fallucca, Federico, Roberto Pignatelli +1
Mathematics · #14J29 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric and Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2305.04545

openalex publication_date 2023/05/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

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.

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