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The Newton polygon of a rational plane curve

hal.structure.identifierDepartment of Mathematics [Berkeley]
hal.structure.identifierDepartamento de Matemática [Buenos Aires]
hal.structure.identifierDepartament d'Algebra i Geometria
dc.contributor.authorD'ANDREA, Carlos
hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorSOMBRA, Martin
dc.date.accessioned2024-04-04T02:42:03Z
dc.date.available2024-04-04T02:42:03Z
dc.date.created2007-11-30
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/191209
dc.description.abstractEnThe 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.
dc.language.isoen
dc.title.enThe Newton polygon of a rational plane curve
dc.typeDocument de travail - Pré-publication
dc.subject.halMathématiques [math]/Théorie des nombres [math.NT]
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
hal.identifierhal-00359281
hal.version1
hal.audienceNon spécifiée
dc.subject.itRational plane curve
dc.subject.itparametrization
dc.subject.itimplicit equation
dc.subject.itNewton polygon
dc.subject.itmixed integral
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-00359281v1
bordeaux.COinSctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.au=D'ANDREA,%20Carlos&SOMBRA,%20Martin&rft.genre=preprint


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