Abstract
Let K be a field, (X iu ) 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 iu ). 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 iS (D,S) and in some sense a complete description of the rigidity of S.
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Vetter, U. Generische determinantielle Singularitäten: Homologische Eigenschaften des Derivationenmoduls. Manuscripta Math 45, 161–191 (1984). https://doi.org/10.1007/BF01169772
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DOI: https://doi.org/10.1007/BF01169772