Affine plane curves with one place at infinity

Masakazu Suzuki

Annales de l'institut Fourier (1999)

  • Volume: 49, Issue: 2, page 375-404
  • ISSN: 0373-0956

Abstract

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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.

How to cite

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Suzuki, Masakazu. "Affine plane curves with one place at infinity." Annales de l'institut Fourier 49.2 (1999): 375-404. <http://eudml.org/doc/75342>.

@article{Suzuki1999,
abstract = {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.},
author = {Suzuki, Masakazu},
journal = {Annales de l'institut Fourier},
keywords = {plane curves; one place at infinity; semigroup criterion; approximate roots},
language = {eng},
number = {2},
pages = {375-404},
publisher = {Association des Annales de l'Institut Fourier},
title = {Affine plane curves with one place at infinity},
url = {http://eudml.org/doc/75342},
volume = {49},
year = {1999},
}

TY - JOUR
AU - Suzuki, Masakazu
TI - Affine plane curves with one place at infinity
JO - Annales de l'institut Fourier
PY - 1999
PB - Association des Annales de l'Institut Fourier
VL - 49
IS - 2
SP - 375
EP - 404
AB - 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.
LA - eng
KW - plane curves; one place at infinity; semigroup criterion; approximate roots
UR - http://eudml.org/doc/75342
ER -

References

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  2. [2] S.S. ABHYANKAR and T.T. MOH, On the semigroup of a meromorphic curve, Proc. Int. Symp. Algebraic Geometry, Kyoto (1977), 249-414. Zbl0408.14010
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  9. [9] C.P. RAMANUJAM, A topological characterization of the affine plane as an algebraic variety, Ann. Math., (2), 94 (1971), 69-88. Zbl0218.14021MR44 #4010
  10. [10] A. SATHAYE and J. STENERSON, On plane polynomial curves, Algebraic geometry and its applications, C.L. Bajaj, ed., Springer, (1994), 121-142. Zbl0809.14022MR95a:14032
  11. [11] M. SUZUKI, Propriété topologique des polynômes de deux variables complexes et automorphismes algébriques de l'espace C2, J. Math. Sci. Japan, 26 (1974), 241-257. Zbl0276.14001MR49 #3188
  12. [12] ZAIDENBERG and LIN, An irreducible simply connected algebraic curve in ℂ2 is equivalent to a quasihomogeneous curve, Soviet Math. Dokl., Vol.28, No.1 (1983), 200-204. Zbl0564.14014MR85i:14018

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