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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Strongly Cohen-Macaulay schemes and residual intersections

Author: Craig Huneke
Journal: Trans. Amer. Math. Soc. 277 (1983), 739-763
MSC: Primary 13H10; Secondary 14M05
MathSciNet review: 694386
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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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Article copyright: © Copyright 1983 American Mathematical Society