2020/01/15 by David Eisenbud, Eisenbud, David, Craig Huneke +3
Mathematics · #13H10 #13N05 #14B12 #14M06 #14M10. Secondary: 13D02 #14M12 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Primary: 13C40
paper · pdf · doi:10.48550/arxiv.2001.05089
openalex publication_date 2020/01/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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'. However, such statements hold for residual intersections of higher codimension only under very restrictive hypotheses, not satisfied even by ideals as simple as the ideal Ln of minors of a generic 2 x 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, we prove that if K is the residual intersection of Ln by 2n-3 general quadratic forms in Ln, then S/K is integrally closed with isolated singularity and In-3 S/K is a self-dual Maximal Cohen-Macaulay module over S/K 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.