New sextics of genus 6 and 10 attaining the Serre bound

Abstract

We provide new examples of curves of genus 6 or 10 attaining the Serre bound. They all belong to the family of sextics introduced in [19] as a generalization of Wiman’s sextics [38] and Edge’s sextics [9]. Our approach is based on a theorem by Kani and Rosen which allows, under certain assumptions, to fully decompose the Jacobian of the curve. With our investigation we are able to update several entries in the table www.manypoints.org, see [37].