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Generators for the derivation modules and the relation ideals of certain curves

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Abstract

LetO be a curve in the affine algebroide-space over a fieldK of characteristic zero. LetD be the module ofK-derivations andP the relation ideal ofO. Generators forD andP are computed in several cases. It is shown in particular that in the case of a monomial curve defined by a sequence ofe positive integers somee−1 of which form an arithmetic sequence, μO ≤ 2e - 3 and μ(P)≤e(e−1)/2.

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References

  1. Bresinsky, H.: On prime ideals with generic zero\(x = t^{n_i }\), Proc. Am. Math. Soc.47, 329–332 (1975)

    Article  MATH  MathSciNet  Google Scholar 

  2. Bresinsky, H.: Symmetric semigroups of integers generated by 4 elements, Manuscr. Math.17, 205–219 (1975)

    Article  MATH  MathSciNet  Google Scholar 

  3. Herzog, J.: Generators and relations of abelian semigroups and semigroup rings, Manuscr. Math.3, 175–193 (1970)

    Article  MATH  MathSciNet  Google Scholar 

  4. Kunz E., Waldi, R.: Über den Derivationenmodul und das Jacobi-Ideal von Kurvensingularitäten, Math. Z.187, 105–123 (1984)

    Article  MATH  MathSciNet  Google Scholar 

  5. Kraft, J.: Singularity of monomial curves, Thesis, Purdue University, 1983

  6. Kraft, J.: Singularity of monomial curves in\(\mathbb{A}^3\) and Gorenstein monomial curves in\(\mathbb{A}^4\), Can. J. Math.37, 872–892 (1985)

    MATH  MathSciNet  Google Scholar 

  7. Moh, T.T.: On generators of ideals, Proc. Am. Math. Soc.77, 309–312 (1979)

    Article  MATH  MathSciNet  Google Scholar 

  8. Patil, D. P., Singh, Balwant: Generators for the derivation modules and the prime ideals of certain curves, Preprint, Tata Inst. Fundam. Res., Bombay, 1990

    Google Scholar 

  9. Patil, D.P.: Certain monomial curves are set-theoretic complete intersections, Manuscr. Math.

  10. Selmer, E.S.: On the linear Diophantine problem of Frobenius, J. Reine Angew. Math.293/294, 1–17 (1977)

    MathSciNet  Google Scholar 

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Authors and Affiliations

  1. School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, 400005, Bombay, India

    Dilip P. Patil & Balwant Singh

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  1. Dilip P. Patil
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  2. Balwant Singh
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Patil, D.P., Singh, B. Generators for the derivation modules and the relation ideals of certain curves. Manuscripta Math 68, 327–335 (1990). https://doi.org/10.1007/BF02568767

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  • DOI: https://doi.org/10.1007/BF02568767

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