On the complexity of the integral closure

Ulrich, Bernd; Vasconcelos, Wolmer

doi:10.1090/S0002-9947-04-03627-X

On the complexity of the integral closure
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by Bernd Ulrich and Wolmer V. Vasconcelos PDF

Trans. Amer. Math. Soc. 357 (2005), 425-442 Request permission

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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