Strongly Cohen-Macaulay schemes and residual intersections

Abstract

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