Strongly Cohen-Macaulay schemes and residual intersections

Huneke, Craig

doi:10.1090/S0002-9947-1983-0694386-5

Strongly Cohen-Macaulay schemes and residual intersections
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Trans. Amer. Math. Soc. 277 (1983), 739-763 Request permission

Abstract:

This paper studies the local properties of closed subschemes $Y$ in Cohen-Macaulay schemes $X$ such that locally the defining ideal of $Y$ in $X$ has the property that its Koszul homology is Cohen-Macaulay. Whenever this occurs $Y$ is said to be strongly Cohen-Macaulay in $X$. This paper proves several facts about such embeddings, chiefly with reference to the residual intersections of $Y$ in $X$. The main result states that any residual intersection of $Y$ in $X$ is again Cohen-Macaulay.

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