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


Author: Wolmer V. Vasconcelos
Journal: Trans. Amer. Math. Soc. 301 (1987), 591-613
MSC: Primary 13H10; Secondary 13C15
DOI: https://doi.org/10.1090/S0002-9947-1987-0882705-X
MathSciNet review: 882705
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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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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1987-0882705-X
Keywords: Linkage, Cohen-Macaulay ideal, Gorenstein ideal, Koszul homology
Article copyright: © Copyright 1987 American Mathematical Society

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