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

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.
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https://hal.archives-ouvertes.fr/hal-00694121
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Submitted on : Thursday, May 3, 2012 - 3:34:12 PM
Last modification on : Tuesday, October 19, 2021 - 10:48:08 AM

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Reynald Lercier, Christophe Ritzenthaler. Hyperelliptic curves and their invariants: geometric, arithmetic and algorithmic aspects. Journal of Algebra, Elsevier, 2012, 372, pp.595-636. ⟨10.1016/j.jalgebra.2012.07.054⟩. ⟨hal-00694121⟩

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