Dans cet article on donne une nouvelle démonstration algébro-géométrique pour le théorème du semi-groupe d’Abhyankar-Moh sur les courbes planes affines avec un point à l’infini et le théorème réciproque dû à Sathaye-Stenerson. Les relations entre les divers invariants de ces courbes sont aussi expliquées géométriquement. Notre nouvelle démonstration donne un algorithme pour classifier les courbes planes affines avec un point à l’infini et un genre donné par ordinateur.
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.
@article{AIF_1999__49_2_375_0,
author = {Suzuki, Masakazu},
title = {Affine plane curves with one place at infinity},
journal = {Annales de l'Institut Fourier},
pages = {375--404},
publisher = {Association des Annales de l{\textquoteright}institut Fourier},
volume = {49},
number = {2},
year = {1999},
doi = {10.5802/aif.1678},
mrnumber = {2000f:14096},
zbl = {0921.14017},
language = {en},
url = {http://www.numdam.org/articles/10.5802/aif.1678/}
}
TY - JOUR AU - Suzuki, Masakazu TI - Affine plane curves with one place at infinity JO - Annales de l'Institut Fourier PY - 1999 SP - 375 EP - 404 VL - 49 IS - 2 PB - Association des Annales de l’institut Fourier UR - http://www.numdam.org/articles/10.5802/aif.1678/ DO - 10.5802/aif.1678 LA - en ID - AIF_1999__49_2_375_0 ER -
%0 Journal Article %A Suzuki, Masakazu %T Affine plane curves with one place at infinity %J Annales de l'Institut Fourier %D 1999 %P 375-404 %V 49 %N 2 %I Association des Annales de l’institut Fourier %U http://www.numdam.org/articles/10.5802/aif.1678/ %R 10.5802/aif.1678 %G en %F AIF_1999__49_2_375_0
Suzuki, Masakazu. Affine plane curves with one place at infinity. Annales de l'Institut Fourier, Tome 49 (1999) no. 2, pp. 375-404. doi : 10.5802/aif.1678. http://www.numdam.org/articles/10.5802/aif.1678/
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