Hyperelliptic curves and their invariants: geometric, arithmetic and   algorithmic aspects
  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. 
Reynald Lercier and Christophe Ritzenthaler
math.NT math.AG