Deformation of Residual Intersections

It is shown that in a Cohen-Macaulay local ring, the generic linkage of an ideal \(I\) is a deformation of the arbitrary linkage of \(I\). This fact does not need \(I\) to be a Cohen-Macaulay ideal. The same holds for \(s\)-residual intersections of \(I\) when \(s\) does not exceed the height of \(I\) by one. Under some slight conditions on \(I\), one further generalizes this principle to encompass any \(s\)-residual intersection.