Core and residual intersections of ideals |
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Authors: | Alberto Corso Claudia Polini Bernd Ulrich |
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Affiliation: | Department of Mathematics, University of Kentucky, Lexington, Kentucky 40506 ; Department of Mathematics, University of Oregon, Eugene, Oregon 97403 ; Department of Mathematics, Michigan State University, East Lansing, Michigan 48824 |
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Abstract: | D. Rees and J. Sally defined the core of an -ideal as the intersection of all (minimal) reductions of . However, it is not easy to give an explicit characterization of it in terms of data attached to the ideal. Until recently, the only case in which a closed formula was known is the one of integrally closed ideals in a two-dimensional regular local ring, due to C. Huneke and I. Swanson. The main result of this paper explicitly describes the core of a broad class of ideals with good residual properties in an arbitrary local Cohen-Macaulay ring. We also find sharp bounds on the number of minimal reductions that one needs to intersect to get the core. |
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Keywords: | Integral closure reductions residual intersections of ideals |
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