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

Related numeric data and programs are available on the web pages of the authorsInternational audienceWe 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