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.
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