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://archive.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://archive.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://archive.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://archive.numdam.org/articles/10.5802/aif.1678/
[1] and , Embeddings of the line in the plane, J. reine angev. Math., 276 (1975), 148-166. | MR | Zbl
[2] and , On the semigroup of a meromorphic curve, Proc. Int. Symp. Algebraic Geometry, Kyoto (1977), 249-414. | Zbl
[3] and , Geometry of plane curves via Tschirnhausen resolution tower, Osaka J. Math., Vol.33, No.4 (1996), 1003-1034. | MR | Zbl
[4] , Finite groups of polynomial automorphisms in the complex affine plane(I), Mem. Fac. Sci. Kyushu Univ., 36 (1982), 85-105. | MR | Zbl
[5] , Minimization of the embeddings of the curves into the affine plane, J. Kyoto Univ., Vol.36, No.2 (1996), 311-329. | MR | Zbl
[6] , Compactifications of C2, Bull. Amer. Math. Soc., 78 (1972), 813-816. | MR | Zbl
[7] and , Smooth plane curves with one place at infinity, to appear in J. Math. Soc. Japan, Vol.49, No.4 (1997). | MR | Zbl
[8] , Complex algebraic curves via their links at infinity, Invent. Math., 98 (1989), 445-489. | MR | Zbl
[9] , A topological characterization of the affine plane as an algebraic variety, Ann. Math., (2), 94 (1971), 69-88. | MR | Zbl
[10] and , On plane polynomial curves, Algebraic geometry and its applications, C.L. Bajaj, ed., Springer, (1994), 121-142. | MR | Zbl
[11] , Propriété topologique des polynômes de deux variables complexes et automorphismes algébriques de l'espace C2, J. Math. Sci. Japan, 26 (1974), 241-257. | MR | Zbl
[12] and , An irreducible simply connected algebraic curve in ℂ2 is equivalent to a quasihomogeneous curve, Soviet Math. Dokl., Vol.28, No.1 (1983), 200-204. | MR | Zbl
Cité par Sources :
