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manuscripta mathematica

, Volume 45, Issue 2, pp 161–191 | Cite as

Generische determinantielle Singularitäten: Homologische Eigenschaften des Derivationenmoduls

  • Udo Vetter
Article

Abstract

Let K be a field, (X u i ) an (m,n)-matrix of indeterminates over K, and r an integer such that i≤r<m≤n. Let P be the localization of K[Xu/i: 1≤i≤m, 1≤u≤n] at the irrelevant maximal ideal, and S the factorring of P with respect to the ideal generated by all (r+1)-minors of (X u i ). By D=DK(S) we denote the module of Kahler-differentials of S over K and by D* its S-dual Homs(D,S). It will be shown that D*. is a Cohen-Macaulay-module if m<nand has depth equal to dim S−1 if m=n. By this we can describe the syzygetic behaviour of D*. In particular one gets a result of Svanes about the vanishing of the modules Ext S i (D,S) and in some sense a complete description of the rigidity of S.

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Copyright information

© Springer-Verlag 1984

Authors and Affiliations

  • Udo Vetter
    • 1
  1. 1.Fachbereich MathematikUniversität Osnabrück Abteilung VechtaVechtaBundesrepublik Deutschland

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