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.
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Hassanzadeh et al. (2024) studied this question.
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