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manuscripta mathematica

, Volume 112, Issue 4, pp 489–509 | Cite as

Symmetric and Rees algebras of Koszul cycles and their Gröbner bases

  • Jürgen HerzogEmail author
  • Zhongming Tang
  • Santiago Zarzuela
Article

Abstract.

In this paper we study the symmetric algebra S(E i ) and Rees algebra R(E i ) of the modules E i of i-cycles of the Koszul complex associated with the sequence of indeterminates \({{x_1,\ldots, x_n}}\) of a polynomial ring \({{K[x_1,\ldots, x_n]}}\). For i=2 and i=n−2 we show that \({{x_1,\ldots, x_n}}\) is a d-sequence on S(E i ) and R(E i ) and we determine Gröbner bases and Sagbi bases related to these algebras.

Keywords

Polynomial Ring Symmetric Algebra Koszul Complex Sagbi Base 
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References

  1. 1.
    Bruns, W., Herzog, J.: Cohen-Macaulay rings, Cambridge: Cambridge University Press, 1993Google Scholar
  2. 2.
    Conca, A., Herzog, J., Valla, G.: Sagbi bases with applications to blow up algebras. J. Reine Angew. Math. 474, 113–138 (1996)MathSciNetzbMATHGoogle Scholar
  3. 3.
    Goto, S., Hayasaka, F., Kurano, K., Nakamura, Y.: Algebras generated by the entries of a certain submatrix and the maximal minors. Preprint, 2002Google Scholar
  4. 4.
    Herzog, J., Restuccia, G., Tang, Z.: L s-sequences and symmetric algebras. Manuscripta Math. 104 (4), 479–501 (2001)CrossRefzbMATHGoogle Scholar
  5. 5.
    Huneke, C.: Symbolic powers of prime ideals and special graded algebras. Comm. Alg. 9 (4), 339–366 (1981)zbMATHGoogle Scholar
  6. 6.
    Huneke, C.: The theory of d-sequences and Powers of ideals. Adv. Math. 46, 249–279 (1982)MathSciNetzbMATHGoogle Scholar
  7. 7.
    Huneke, C., Ulrich, B.: Divisor class groups and deformations. Am. J. Math. 107 (6), 1265–1303 (1985)zbMATHGoogle Scholar
  8. 8.
    Möller, H. M., Mora, F.: New constructive methods in classical ideal theory. J. Alg. 100, 138–178 (1986)MathSciNetzbMATHGoogle Scholar
  9. 9.
    Simis, A., Ulrich, B., Vasconcelos, W.V.: Jacobian dual fibrations. Am. J. Math. 115 (1), 47–75 (1993)zbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Jürgen Herzog
    • 1
    Email author
  • Zhongming Tang
    • 2
  • Santiago Zarzuela
    • 3
  1. 1.FB6 Mathematik und InformatikUniversität-GHS-EssenEssenGermany
  2. 2.Department of MathematicsSuzhou UniversitySuzhouP.R. China
  3. 3.Departament d’Àlgebra i GeometriaUniversitat de BarcelonaBarcelonaSpain

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