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Mathematics of Computation

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Computing the tight closure in dimension two

Author: Holger Brenner
Journal: Math. Comp. 74 (2005), 1495-1518
MSC (2000): Primary 13A35; Secondary 14H60
Published electronically: January 27, 2005
MathSciNet review: 2137014
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Abstract: We study computational aspects of the tight closure of a homogeneous primary ideal in a two-dimensional normal standard-graded domain. We show how to use slope criteria for the sheaf of relations for generators of the ideal to compute its tight closure. In particular, our method gives an algorithm to compute the tight closure of three elements under the condition that we are able to compute the Harder-Narasimhan filtration. We apply this to the computation of $(x^{a},y^{a},z^{a})^*$ in $K[x,y,z]/(F)$, where $F$ is a homogeneous polynomial.

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Additional Information

Holger Brenner
Affiliation: Department of Pure Mathematics, University of Sheffield, Hicks Building, Hounsfield Road, Sheffield S3 7RH, United Kingdom
MR Author ID: 322383

Received by editor(s): March 10, 2003
Received by editor(s) in revised form: April 11, 2004
Published electronically: January 27, 2005
Article copyright: © Copyright 2005 American Mathematical Society