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Pré-Publication, Document De Travail Année : 2023

Invariants of genus 4 curves

Invariants des courbes de genre 4

Résumé

The present paper gives an explicit classification of the isomorphism classes of non-hyperelliptic genus 4 curves over an algebraically closed field of characteristic 0. A non-hyperelliptic genus 4 curve lies on a quadric in $\mathbb{P^3}$ of rank 3 or 4. In the case of rank 3, we give a set of 60 invariants which classify the isomorphism classes, and in the case of rank 4, we find 65 invariants. These invariants are defined by transvectants and can be efficiently computed on a given example.
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Dates et versions

hal-04224362 , version 1 (02-10-2023)

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Paternité

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Thomas Bouchet. Invariants of genus 4 curves. 2023. ⟨hal-04224362⟩
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