Computing the nonfree locus of the moduli space of arrangements and Terao’s freeness conjecture
Barakat M, Kühne L (2023)
Mathematics of Computation 92: 1413-1452.
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Autor*in
Barakat, Mohamed;
Kühne, LukasUniBi 
Einrichtung
Abstract / Bemerkung
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.
Stichworte
Rank 3 simple matroids;
Terao?s freeness conjecture;
Fitting ideals;
multiarrangements
Erscheinungsjahr
2023
Zeitschriftentitel
Mathematics of Computation
Band
92
Seite(n)
1413-1452
ISSN
0025-5718
eISSN
1088-6842
Page URI
https://pub.uni-bielefeld.de/record/2969558
Zitieren
Barakat M, Kühne L. Computing the nonfree locus of the moduli space of arrangements and Terao’s freeness conjecture. Mathematics of Computation. 2023;92:1413-1452.
Barakat, M., & Kühne, L. (2023). Computing the nonfree locus of the moduli space of arrangements and Terao’s freeness conjecture. Mathematics of Computation, 92, 1413-1452. https://doi.org/10.1090/mcom/3812
Barakat, Mohamed, and Kühne, Lukas. 2023. “Computing the nonfree locus of the moduli space of arrangements and Terao’s freeness conjecture”. Mathematics of Computation 92: 1413-1452.
Barakat, M., and Kühne, L. (2023). Computing the nonfree locus of the moduli space of arrangements and Terao’s freeness conjecture. Mathematics of Computation 92, 1413-1452.
Barakat, M., & Kühne, L., 2023. Computing the nonfree locus of the moduli space of arrangements and Terao’s freeness conjecture. Mathematics of Computation, 92, p 1413-1452.
M. Barakat and L. Kühne, “Computing the nonfree locus of the moduli space of arrangements and Terao’s freeness conjecture”, Mathematics of Computation, vol. 92, 2023, pp. 1413-1452.
Barakat, M., Kühne, L.: Computing the nonfree locus of the moduli space of arrangements and Terao’s freeness conjecture. Mathematics of Computation. 92, 1413-1452 (2023).
Barakat, Mohamed, and Kühne, Lukas. “Computing the nonfree locus of the moduli space of arrangements and Terao’s freeness conjecture”. Mathematics of Computation 92 (2023): 1413-1452.
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arXiv: 2112.13065
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