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Plane Polynomial Curves

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Abstract

We study some properties of generator sequences of planar semigroups and give a method of construction of plane curves with one place at infinity with given generator sequences. We also discuss similar questions for polynomial curves.

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References

  1. Abhyankar, S. S. “Expansion Techniques in Algebraic Geometry” Tata Institute of Fundamental Research, 1977.

    MATH  Google Scholar 

  2. Abhyankar, S. S. On the semigroup of a meromorphic curve, Proc. Int. Symp. on Algebraic Geometry, Kyoto 1977, 249–414.

    Google Scholar 

  3. Abhyankar, S., S. Irreducibility criterion for germs of analytic functions of Two complex Variables. Advances in Mathematics, 74(2), (1989), 190–257.

    Article  MathSciNet  MATH  Google Scholar 

  4. Abhyankar, S. S., and Moh, T. T., Newton-Puiseux expansion and Tschirnhausen transformation I, J. Reine Angew. Math. 260 (1973), 47–83.

    Article  MathSciNet  Google Scholar 

  5. Abhyankar, S. S., and Moh, T. T., Newton-Puiseux expansion and Tschirnhausen transformation II, J. Reine Angew. Math. 261 (1973), 29–54.

    MathSciNet  Google Scholar 

  6. Abhyankar, S. S., and Moh, T. T., Embeddings of the line in the plane, J. Reine Angew. Math. 276 (1975),148–166.

    MathSciNet  MATH  Google Scholar 

  7. Abhyankar, S. S., and Singh, B., Embeddings of certain curves in the affine plane, Amer. J. Math. 100(1978), 99–175.

    Article  MathSciNet  MATH  Google Scholar 

  8. Birch B., Chowla, S., Hall, M., and Schinzel, A., On the difference x 3 — y 2K. Norske Vid. Selsk. Forrh. (Trondheim), 38(1965), 65–69.

    MathSciNet  MATH  Google Scholar 

  9. Davenport, H., On f 3 (t) — g 2 (t), K. Norske Vid. Selsk. Forrh. (Trondheim), 38(1965), 86–87.

    MathSciNet  MATH  Google Scholar 

  10. Lang, S., Old and new conjectured diophantine inequalities, Bull. Amer. Math. Soc. (N. S.) 23(1) (1990),37–75.

    Article  MathSciNet  MATH  Google Scholar 

  11. Macdonald, I. G. “Symmetric Functions and Hall Polynomials.” Oxford University Press, New York, 1979.

    MATH  Google Scholar 

  12. Mason, R. C., Equations over function fields, Springe Lecture Notes 1068 (1984)149–157, in Number Theory, proceedings of the Noordwijkerhout, 1983.

    Google Scholar 

  13. Moh, T. T., On characteristic paris of algebroid plane curves for characteristic p, Bull. Inst. Math. Acad. Sinica, 1(1973), 75–91.

    MathSciNet  MATH  Google Scholar 

  14. Moh, T. T., On approximate roots of a polynomial, J. Reine Angew. Math. 278(1975), 301–306.

    Article  MathSciNet  Google Scholar 

  15. Moh, T. T., On then concept of approximate roots for algebra, J. Alg. 65(1980),301–306.

    Article  MathSciNet  Google Scholar 

  16. Moh, T. T., On two fundamental theorems for the concept of approximate roots, J. Math. Soc. Japan 34(1982), 637–652.

    Article  MathSciNet  MATH  Google Scholar 

  17. Moh, T. T. On analytic irreducibility at ∞ Proc. Amer. Math. Soc. 44(1982), 22–24.

    MathSciNet  Google Scholar 

  18. Moh, T. T., On the jacobian conjecture and the configuration of roots, J. Reine Angew. Math. 340(1983), 331–340.

    MathSciNet  Google Scholar 

  19. Richman, D. R., On the computation of mainimal polynomials, J. of Algebra, 103(1986), 1–17.

    Article  MathSciNet  MATH  Google Scholar 

  20. Russell, P. Hamburger-Noether expansions and approximate roots of polynomials, manuscripta math. 31(1980), 25–95.

    Article  MathSciNet  MATH  Google Scholar 

  21. Sathaye, A., On planar curves, Amer. J. Math. 99(5)(1977),1105–1135.

    Article  MathSciNet  Google Scholar 

  22. Sathaye, A., Generalized Newton-Puiseux expansion and Abhyankar– Moh semigroup theorem, Invent, math. 74(1983), 149–157.

    Article  MathSciNet  MATH  Google Scholar 

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© 1994 Springer-Verlag New York, Inc.

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Sathaya, A., Stenerson, J. (1994). Plane Polynomial Curves. In: Bajaj, C.L. (eds) Algebraic Geometry and its Applications. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-2628-4_6

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  • DOI: https://doi.org/10.1007/978-1-4612-2628-4_6

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4612-7614-2

  • Online ISBN: 978-1-4612-2628-4

  • eBook Packages: Springer Book Archive

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