D'ANDREA, Carlos; SOMBRA, Martin

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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]

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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.< Leer menos

Palabras clave en italiano

Rational plane curve

parametrization

implicit equation

Newton polygon

mixed integral

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The Newton polygon of a rational plane curve

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