Hyperelliptic curves and their invariants: geometric, arithmetic and algorithmic aspects
Number Theory
2011-11-18 v1 Algebraic Geometry
Abstract
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.
Cite
@article{arxiv.1111.4152,
title = {Hyperelliptic curves and their invariants: geometric, arithmetic and algorithmic aspects},
author = {Reynald Lercier and Christophe Ritzenthaler},
journal= {arXiv preprint arXiv:1111.4152},
year = {2011}
}
Comments
46 pages ; related programs are available on the web pages of the authors