D'ANDREA, Carlos; SOMBRA, Martin

Métadonnées

Licence d’utilisation du document

D'ANDREA, Carlos
Department of Mathematics [Berkeley]
Departamento de Matemática [Buenos Aires]
Departament d'Algebra i Geometria

SOMBRA, Martin
Institut de Mathématiques de Bordeaux [IMB]

Langue

Document de travail - Pré-publication

Résumé en anglais

The Newton polygon of the implicit equation of a rational plane curve is explicitly determined by the multiplicities of any of its parametrizations. We give an intersection-theoretical proof of this fact based on a reﬁnement of the Kuˇsnirenko- Bernˇstein theorem. We apply this result to the determination of the Newton polygon of a curve parameterized by generic Laurent polynomials or by generic rational func- tions, with explicit genericity conditions. We also show that the variety of rational curves with given Newton polygon is unirational and we compute its dimension. As a consequence, we obtain that any convex lattice polygon with positive area is the Newton polygon of a rational plane curve.< Réduire

Mots clés en italien

Rational plane curve

parametrization

implicit equation

Newton polygon

mixed integral

Métadonnées

Partager cette publication !

Licence d’utilisation du document

The Newton polygon of a rational plane curve

Langue

Résumé en anglais

Mots clés en italien

URI

Origine

Unités de recherche