Displaying similar documents to “Some properties of plane curves”

Affine plane curves with one place at infinity

Masakazu Suzuki (1999)

Annales de l'institut Fourier

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In this paper we give a new algebro-geometric proof to the semi-group theorem due to Abhyankar-Moh for the affine plane curves with one place at infinity and its inverse theorem due to Sathaye-Stenerson. The relations between various invariants of these curves are also explained geometrically. Our new proof gives an algorithm to classify the affine plane curves with one place at infinity with given genus by computer.

The distance of a curve to its control polygon.

Jesús Miguel Carnicer, M.S. Floater, Juan M. Peña (2002)

RACSAM

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Recientemente, Nairn, Peters y Lutterkort han acotado la distancia entre una curva de Bézier y su polígono de control en términos de las diferencias entre los puntos de control. Mostramos cómo extender dichas cotas a muchos tipos de curvas utilizadas en el Diseño Geométrico.

Curves on a smooth quadric.

S. Giuffrida, R. Maggioni (2003)

Collectanea Mathematica

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We associate to every curve on a smooth quadric a polynomial equation that defines it as a divisor; this polynomial is defined through a matrix. In this way we can study several properties of these curves; in particular we can give a geometrical meaning to the rank of the matrix which defines the curve.