In Cohen-Macaulay local rings, generic linkage of an ideal I is a deformation of arbitrary linkage of I, with the same holding for s-residual intersections under height conditions.
Koszul homology and blowing-up rings
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Deformation of Residual Intersections
In Cohen-Macaulay local rings, generic linkage of an ideal I is a deformation of arbitrary linkage of I, with the same holding for s-residual intersections under height conditions.