The 2-Weierstrass points of genus 3 hyperelliptic curves with extra automorphisms

Abstract

For each group $G$, $(|G|>2)$ \, which acts as a full automorphism group on a genus 3 hyperelliptic curve, we determine the family of curves which have 2-Weierstrass points. Such families of curves are explicitly determined in terms of the absolute invariants of binary octavics. The 1-dimensional families that we discover have the property that they contain only genus 0 components.

References in corpus (2)

• Bielliptic curves of genus 3 in the hyperelliptic moduli
• Some remarks on the hyperelliptic moduli of genus 3

Cited by in corpus (1)

• From hyperelliptic to superelliptic curves