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- Title
Residual intersections and linear powers.
- Authors
Eisenbud, David; Huneke, Craig; Ulrich, Bernd
- Abstract
If I is an ideal in a Gorenstein ring S, and S/I is Cohen-Macaulay, then the same is true for any linked ideal I'; but such statements hold for residual intersections of higher codimension only under restrictive hypotheses, not satisfied even by ideals as simple as the ideal L_{n} of minors of a generic 2 \times n matrix when n>3. In this paper we initiate the study of a different sort of Cohen-Macaulay property that holds for certain general residual intersections of the maximal (interesting) codimension, one less than the analytic spread of I. For example, suppose that K is the residual intersection of L_{n} by 2n-4 general quadratic forms in L_{n}. In this situation we analyze S/K and show that I^{n-3}(S/K) is a self-dual maximal Cohen-Macaulay S/K-module with linear free resolution over S. The technical heart of the paper is a result about ideals of analytic spread 1 whose high powers are linearly presented.
- Subjects
GORENSTEIN rings; QUADRATIC forms
- Publication
Transactions of the American Mathematical Society, Series B, 2023, Vol 10, p1333
- ISSN
2330-0000
- Publication type
Article
- DOI
10.1090/btran/127