HAL : hal-00359281, version 1

Fiche détaillée

Récupérer au format BibTeX - EndNote - TEI - RefWorks -

The Newton polygon of a rational plane curve

Carlos D'Andrea 1, 2, 3, Martin Sombra 4

(30/11/2007)

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.

1 :	Department of Mathematics
	University of California at Berkeley
2 :	Departamento de Matemática (DM-UBA)
	Universidad de Buenos Aires
3 :	Departament d'Algebra i Geometria
	Facultat de Matematiques, Universitat de Barcelona
4 :	Institut de Mathématiques de Bordeaux (IMB)
	CNRS : UMR5251 – Université Sciences et Technologies - Bordeaux I – Université Victor Segalen - Bordeaux II

Domaine

:

Mathématiques/Théorie des nombres

Mots Clés : Rational plane curve – parametrization – implicit equation – Newton polygon – mixed integral

hal-00359281, version 1

http://hal.archives-ouvertes.fr/hal-00359281

oai:hal.archives-ouvertes.fr:hal-00359281

Contributeur : Catherine Vrit <>

Soumis le : Vendredi 6 Février 2009, 14:39:02

Dernière modification le : Dimanche 8 Février 2009, 21:40:33