Journal of Commutative Algebra
- J. Commut. Algebra
- Volume 12, Number 1 (2020), 77-86.
A Gröbner basis for the graph of the reciprocal plane
Given the complement of a hyperplane arrangement, let be the closure of the graph of the map inverting each of its defining linear forms. The characteristic polynomial manifests itself in the Hilbert series of in two different-seeming ways, one due to Terao and the other to Huh and Katz. We define an extension of the no broken circuit complex of a matroid and use it to give a direct Gröbner basis argument that the polynomials extracted from the Hilbert series in these two ways agree.
J. Commut. Algebra, Volume 12, Number 1 (2020), 77-86.
Received: 13 May 2017
Revised: 11 June 2017
Accepted: 18 June 2017
First available in Project Euclid: 13 May 2020
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Primary: 13F55: Stanley-Reisner face rings; simplicial complexes [See also 55U10] 13P10: Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) 05E45: Combinatorial aspects of simplicial complexes 52C35: Arrangements of points, flats, hyperplanes [See also 32S22]
Fink, Alex; Speyer, David E.; Woo, Alexander. A Gröbner basis for the graph of the reciprocal plane. J. Commut. Algebra 12 (2020), no. 1, 77--86. doi:10.1216/jca.2020.12.77. https://projecteuclid.org/euclid.jca/1589335256