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Creators/Authors contains: "Huneke, Craig"

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  1. ; ; (, Transactions of the American Mathematical Society)
    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 Ln of minors of a generic 2 × 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 Ln by 2n − 4 general quadratic forms in Ln. In this situation we analyze S/K and show that In−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. 
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  2. ; ; (, Advances in Mathematics)
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  3. ; ; (, Transactions of the American Mathematical Society, Series B)
    If I I is an ideal in a Gorenstein ring S S , and S / I S/I is Cohen-Macaulay, then the same is true for any linked ideal I ′ 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 L_{n} of minors of a generic 2 ×<#comment/> n 2 \times n matrix when n > 3 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 I . For example, suppose that K K is the residual intersection of L n L_{n} by 2 n −<#comment/> 4 2n-4 general quadratic forms in L n L_{n} . In this situation we analyze S / K S/K and show that I n −<#comment/> 3 ( S / K ) I^{n-3}(S/K) is a self-dual maximal Cohen-Macaulay S / K S/K -module with linear free resolution over S S . The technical heart of the paper is a result about ideals of analytic spread 1 whose high powers are linearly presented. 
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  4. ; ; (, Michigan Mathematical Journal)
    Building on previous work by the same authors, we show that certain ideals defining Gorenstein rings have expected resurgence and thus satisfy the stable Harbourne conjecture. In prime characteristic, we can take any radical ideal defining a Gorenstein ring in a regular ring, provided that its symbolic powers are given by saturations with the maximal ideal. Although this property is not suitable for reduction to characteristic p, we show that a similar result holds in equicharacteristic 0 under the additional hypothesis that the symbolic Rees algebra of I is Noetherian. 
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  5. ; ; ; (, Advances in Mathematics)
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  6. ; ; ; ; ; ; ; ; ; ; et al (, Notices of the American Mathematical Society)
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  7. ; ; (, Acta Mathematica Vietnamica)
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  8. ; ; ; (, Journal of Pure and Applied Algebra)
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