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Symmetric and Rees algebras of Koszul cycles and their Gröbner bases

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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.

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Authors and Affiliations

  1. FB6 Mathematik und Informatik, Universität-GHS-Essen, Postfach, 103764 45117, Essen, Germany

    Jürgen Herzog

  2. Department of Mathematics, Suzhou University, Suzhou, 2150006, P.R. China

    Zhongming Tang

  3. Departament d’Àlgebra i Geometria, Universitat de Barcelona, Gran Via 585, E-08007, Barcelona, Spain

    Santiago Zarzuela

Authors
  1. Jürgen Herzog
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  2. Zhongming Tang
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  3. Santiago Zarzuela
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Corresponding author

Correspondence to Jürgen Herzog.

Additional information

Mathematics Subject Classification (2000): 13A30, 13D02, 13H10, 13P10

The second author is grateful to the National Natural Science Foundation of China for support.

Part of this work was made while the third author was visiting the Fachbereich Mathematik und Informatik der Universität Essen, to which he would like to thank for its hospitality.

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Herzog, J., Tang, Z. & Zarzuela, S. Symmetric and Rees algebras of Koszul cycles and their Gröbner bases. manuscripta math. 112, 489–509 (2003). https://doi.org/10.1007/s00229-003-0420-2

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  • DOI: https://doi.org/10.1007/s00229-003-0420-2

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