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Core and residual intersections of ideals
Author(s):
Alberto
Corso;
Claudia
Polini;
Bernd
Ulrich
Journal:
Trans. Amer. Math. Soc.
354
(2002),
2579-2594.
MSC (2000):
Primary 13H10;
Secondary 13A30, 13B22, 13C40, 13D45
Posted:
February 1, 2002
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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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Additional Information:
Alberto
Corso
Affiliation:
Department of Mathematics, University of Kentucky, Lexington, Kentucky 40506
Email:
corso@ms.uky.edu
Claudia
Polini
Affiliation:
Department of Mathematics, University of Oregon, Eugene, Oregon 97403
Address at time of publication:
Department of Mathematics, University of Notre Dame, Notre Dame, Indiana 46556
Email:
cpolini@nd.edu
Bernd
Ulrich
Affiliation:
Department of Mathematics, Michigan State University, East Lansing, Michigan 48824
Address at time of publication:
Department of Mathematics, Purdue University, West Lafayette, Indiana 47907
Email:
ulrich@math.purdue.edu
DOI:
10.1090/S0002-9947-02-02908-2
PII:
S 0002-9947(02)02908-2
Keywords:
Integral closure,
reductions,
residual intersections of ideals
Received by editor(s):
April 10, 2001
Posted:
February 1, 2002
Additional Notes:
The first author was partially supported by the NATO/CNR Advanced Fellowships Programme during an earlier stage of this work. The second and third authors were partially supported by the NSF
Dedicated:
To Professor Craig Huneke on the occasion of his fiftieth birthday
Copyright of article:
Copyright
2002,
American Mathematical Society
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