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The 2-Weierstrass points of genus 3 hyperelliptic curves with extra automorphisms (1307.8177v2)
Published 31 Jul 2013 in math.AG
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.