## Journal of Commutative Algebra

### A Gröbner basis for the graph of the reciprocal plane

#### Abstract

Given the complement of a hyperplane arrangement, let $Γ$ 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 $Γ$ 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.

#### Article information

Source
J. Commut. Algebra, Volume 12, Number 1 (2020), 77-86.

Dates
Revised: 11 June 2017
Accepted: 18 June 2017
First available in Project Euclid: 13 May 2020

https://projecteuclid.org/euclid.jca/1589335256

Digital Object Identifier
doi:10.1216/jca.2020.12.77

Mathematical Reviews number (MathSciNet)
MR4097057

#### Citation

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