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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


Computing the tight closure in dimension two
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by Holger Brenner PDF
Math. Comp. 74 (2005), 1495-1518 Request permission


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
  • Email:
  • Received by editor(s): March 10, 2003
  • Received by editor(s) in revised form: April 11, 2004
  • Published electronically: January 27, 2005
  • © Copyright 2005 American Mathematical Society
  • Journal: Math. Comp. 74 (2005), 1495-1518
  • MSC (2000): Primary 13A35; Secondary 14H60
  • DOI:
  • MathSciNet review: 2137014