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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 nonfree locus of the moduli space of arrangements and Terao’s freeness conjecture
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by Mohamed Barakat and Lukas Kühne HTML | PDF
Math. Comp. 92 (2023), 1431-1452


In this paper, we show how to compute, using Fitting ideals, the nonfree locus of the moduli space of arrangements of a rank $3$ simple matroid, i.e., the subset of all points of the moduli space which parametrize nonfree arrangements. Our approach relies on the so-called Ziegler restriction and Yoshinaga’s freeness criterion for multiarrangements. We use these computations to verify Terao’s freeness conjecture for rank $3$ central arrangements with up to $14$ hyperplanes in any characteristic.
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Additional Information
  • Mohamed Barakat
  • Affiliation: Department of mathematics, University of Siegen, 57068 Siegen, Germany
  • MR Author ID: 706483
  • ORCID: 0000-0003-3642-4190
  • Email:
  • Lukas Kühne
  • Affiliation: Max Planck Institute for Mathematics in the Sciences, Inselstr. 22, 04103 Leipzig, Germany; and Fakultät für Mathematik, Universität Bielefeld, Bielefeld, Germany
  • Email:
  • Received by editor(s): January 24, 2022
  • Received by editor(s) in revised form: September 30, 2022
  • Published electronically: January 31, 2023
  • Additional Notes: An extended abstract of this paper appeared in the Oberwolfach workshop report 5/2021 and in the Computeralgebra Rundbrief Ausgabe 68.
  • © Copyright 2023 by the authors.
  • Journal: Math. Comp. 92 (2023), 1431-1452
  • MSC (2020): Primary 05B35, 52C35, 32S22, 14Q20
  • DOI:
  • MathSciNet review: 4550333