Hyperelliptic curves and their invariants: geometric, arithmetic and algorithmic aspects

By Reynald Lercier, Christophe Ritzenthaler. 2011

78 citations recorded by the source corpus.

We apply classical invariant theory of binary forms to explicitly characterize isomorphism classes of hyperelliptic curves of small genus and, conversely, propose algorithms for reconstructing hyperelliptic models from given invariants. We focus on genus 3 hyperelliptic curves. Both geometric and arithmetic aspects are considered.

Subfields: Computational Theory and Mathematics, Geometry and Topology, Information Systems

View Paper: https://www.semanticscholar.org/paper/603f768f7225b31b429761b136724933c28cf522