Koszul homology and the structure of low codimension Cohen-Macaulay ideals

Vasconcelos, Wolmer V.

doi:10.1090/S0002-9947-1987-0882705-X

Koszul homology and the structure of low codimension Cohen-Macaulay ideals
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Trans. Amer. Math. Soc. 301 (1987), 591-613 Request permission

Abstract:

The relationship between the properties of the Koszul homology modules of two ideals connected by linkage is studied. If the ideal $I$ is either (i) a Cohen-Macaulay ideal of codimension 3, or (ii) a Gorenstein ideal of codimension 4, the one-dimensional Koszul module carries considerable information on the structural nature of the linkage class of $I$ in case (i), or on the conormal module of $I$ in case (ii). Emphasis is given to the verification of the properties by computation.

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