A strategy and a new operator to generate covariants in small characteristic

Ulpat Rovetta, Florent

Publications mathématiques de Besançon. Algèbre et théorie des nombres (2018), pp. 85-99.

Nous présentons quelques résultats nouveaux sur les covariants en petite caractéristique. Dans la section 1, nous expliquons une méthode pour construire des covariants en utilisant une approche similaire à celle de Sturmfels. Nous appliquons notre méthode pour obtenir un système séparant pour les covariants des formes quartiques binaires en caractéristique 3. Dans la section 2, nous construisons un nouvel opérateur sur les covariants lorsque la caractéristique est petite par rapport au degré des formes.

We present some new results about covariants in small characteristic. In Section 1, we give a method to construct covariants using an approach similar to Sturmfels. We apply our method to find a separating system of covariants for binary quartics in characteristic $3$. In Section 2, we construct a new operator on covariants when the characteristic is small compared to the degree of the form.

Classification : 13A50, 14H45
Mots clés : Positive and small characteristic, syzygies, generating system of covariants, separating system of covariants.

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