The Newton polygon of a rational plane curve
| hal.structure.identifier | Department of Mathematics [Berkeley] | |
| hal.structure.identifier | Departamento de Matemática [Buenos Aires] | |
| hal.structure.identifier | Departament d'Algebra i Geometria | |
| dc.contributor.author | D'ANDREA, Carlos | |
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | SOMBRA, Martin | |
| dc.date.accessioned | 2024-04-04T02:42:03Z | |
| dc.date.available | 2024-04-04T02:42:03Z | |
| dc.date.created | 2007-11-30 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/191209 | |
| dc.description.abstractEn | 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. | |
| dc.language.iso | en | |
| dc.title.en | The Newton polygon of a rational plane curve | |
| dc.type | Document de travail - Pré-publication | |
| dc.subject.hal | Mathématiques [math]/Théorie des nombres [math.NT] | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| hal.identifier | hal-00359281 | |
| hal.version | 1 | |
| hal.audience | Non spécifiée | |
| dc.subject.it | Rational plane curve | |
| dc.subject.it | parametrization | |
| dc.subject.it | implicit equation | |
| dc.subject.it | Newton polygon | |
| dc.subject.it | mixed integral | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-00359281v1 | |
| bordeaux.COinS | ctx_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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