Smooth plane curves with one place at infinity

Yuji NAKAZAWA; Mutsuo OKA

doi:10.2969/jmsj/04940663

Yuji NAKAZAWA, Mutsuo OKA

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JOURNAL FREE ACCESS

1997 Volume 49 Issue 4 Pages 663-687

DOI https://doi.org/10.2969/jmsj/04940663

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Published: 1997 Received: August 07, 1995 Available on J-STAGE: October 20, 2006 Accepted: - Advance online publication: - Revised: -
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Date of correction: October 20, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 1) S. S. Abhyankar and T. Moh, Newton-Puiseux expansion and generalized Tschirnhausen transformation I, J. Reine Angew. Math., 260 (1973), 47-83. Smooth plane curves with one plane at infinity 687
2) S. S. Abhyankar and T. Moh, Newton-Puiseux expansion and generalized Tschirnhausen transformation II, J. Reine Angew. Math., 261 (1973), 29-54.
3) S. S. Abhyankar and T. Moh, Embeddings of line in the plane, J. Reine Angew. Math., 276 (1975), 148-166.
4) N. A'Campo and M. Oka, Geometry of plane curves via Tschirnhausen resolution tower, Osaka J. Math., 33 (1996), 1003-1033.
5) P. Jaworski, Normal forms and bases of local rings of irreducible germs of functions of two variables, J. Soviet Math., 50 (1990), 1350-1364.
6) J. Milnor, Singular Points of Complex Hypersurface, Annals Math. Studies, vol. 61, Princeton Univ. Press, Princeton, 1968.
7) M. Miyanishi, Minimization of the embeddings of the curves into the affine plane, J. Math. Kyoto Univ., 36 (1996), 311-329.
8) T. T. Moh, On analytic irreducibility at ∞ of a pencil of curves, Proc. Amer. Soc., 44 (1974), 22-24.
9) W. D. Neumann, Complex algebraic curves via their links at infinity, Invent. Math., 98 (1989), 445-489.
10) T. Oda, Convex Bodies and Algebraic Geometry, Springer, Berlin-Heidelberg-New York, 1987.
11) M. Oka, Polynomial normal form of a plane curve with a given weight sequence, Chinese Quart. J. Math., 10, no. 4 (1995), 53-61.
12) M. Suzuki, Propriétés topologiques des polynômes de deux variables complexes, et automorphismes algebriques de l'espace C², Journal of Math. Soc. Japan, 26 (1974), 241-257.
13) E.W.v. Tschirnhausen, Acta eruditorum, Leiptiz, 1683.

Right : [1] S. S. Abhyankar and T. Moh, Newton-Puiseux expansion and generalized Tschirnhausen transformation I, J. Reine Angew. Math., 260 (1973), 47-83.
[2] S. S. Abhyankar and T. Moh, Newton-Puiseux expansion and generalized Tschirnhausen transformation II, J. Reine Angew. Math., 261 (1973), 29-54.
[3] S. S. Abhyankar and T. Moh, Embeddings of line in the plane, J. Reine Angew. Math., 276 (1975), 148-166.
[4] N. A'Campo and M. Oka, Geometry of plane curves via Tschirnhausen resolution tower, Osaka J. Math., 33 (1996), 1003-1033.
[5] P. Jaworski, Normal forms and bases of local rings of irreducible germs of functions of two variables, J. Soviet Math., 50 (1990), 1350-1364.
[6] J. Milnor, Singular Points of Complex Hypersurface, Annals Math. Studies, vol. 61, Princeton Univ. Press, Princeton, 1968.
[7] M. Miyanishi, Minimization of the embeddings of the curves into the affine plane, J. Math. Kyoto Univ., 36 (1996), 311-329.
[8] T. T. Moh, On analytic irreducibility at ∞ of a pencil of curves, Proc. Amer. Soc., 44 (1974), 22-24.
[9] W. D. Neumann, Complex algebraic curves via their links at infinity, Invent. Math., 98 (1989), 445-489.
[10] T. Oda, Convex Bodies and Algebraic Geometry, Springer, Berlin-Heidelberg-New York, 1987.
[11] M. Oka, Polynomial normal form of a plane curve with a given weight sequence, Chinese Quart. J. Math., 10, no. 4 (1995), 53-61.
[12] M. Suzuki, Propriétés topologiques des polynômes de deux variables complexes, et automorphismes algébriques de l'espace C², Journal of Math. Soc. Japan, 26 (1974), 241-257.
[13] E. W. v. Tschirnhausen, Acta eruditorum, Leiptiz, 1683.

Date of correction: October 20, 2006 Reason for correction: - Correction: PDF FILE Details: -

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