Covariant reconstruction of forms from their invariants
Résumé
Let $K$ be an algebraically closed field of characteristic $0$ and $f$ be a homogeneous polynomial. We provide an explicit algorithm, which, given the invariants of a generic $f$ under the action of $\mathrm{GL}_n(K)$ returns a polynomial in the orbit of $f$. We derive a specific algorithm for the reconstruction of a generic non-hyperelliptic curve of genus 4 from its invariants, as well as a direct reconstruction algorithm for generic non-hyperelliptic curves of genus 3 from their Dixmier-Ohno invariants.
Origine : Fichiers produits par l'(les) auteur(s)
licence : CC BY - Paternité
licence : CC BY - Paternité