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On the complexity of the integral closure

Authors: Bernd Ulrich and Wolmer V. Vasconcelos
Journal: Trans. Amer. Math. Soc. 357 (2005), 425-442
MSC (2000): Primary 13B22; Secondary 13C15, 13H15, 13P10
Published electronically: September 23, 2004
MathSciNet review: 2095616
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Abstract: The computation of the integral closure of an affine ring has been the focus of several modern algorithms. We will treat here one related problem: the number of generators the integral closure of an affine ring may require. This number, and the degrees of the generators in the graded case, are major measures of cost of the computation. We prove several polynomial type bounds for various kinds of algebras, and establish in characteristic zero an exponential type bound for homogeneous algebras with a small singular locus.

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Additional Information

Bernd Ulrich
Affiliation: Department of Mathematics, Purdue University, West Lafayette, Indiana 47907-1395

Wolmer V. Vasconcelos
Affiliation: Department of Mathematics, Rutgers University, 110 Frelinghuysen Rd., Piscataway, New Jersey 08854-8019

Keywords: Cohen-Macaulay ring, integral closure, isolated singularity, Jacobian ideal, multiplicity
Received by editor(s): May 10, 2002
Published electronically: September 23, 2004
Additional Notes: The authors were partially supported by the NSF
Dedicated: Dedicated to Aron Simis on the occasion of his sixtieth birthday
Article copyright: © Copyright 2004 American Mathematical Society

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