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

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

2011-11-17

arxiv.org/abs/1111.4152v1

Mathematics

Number Theory

46 pages ; related programs are available on the web pages of the authors

Scientific paper

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.

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