A Broken Circuit Ring
Combinatorics
2007-05-23 v2 Commutative Algebra
Abstract
Given a matroid M represented by a linear subspace L in n-space (equivalently by an arrangement of n hyperplanes in L), we define a graded ring R(L) which degenerates to the Stanley-Reisner ring of the broken circuit complex for any choice of ordering of the ground set. In particular, R(L) is Cohen-Macaulay, and may be used to compute the h-vector of the broken circuit complex of M. We give a geometric interpretation of Spec R(L), as well as a stratification indexed by the flats of M.
Cite
@article{arxiv.math/0410069,
title = {A Broken Circuit Ring},
author = {Nicholas J. Proudfoot and David E. Speyer},
journal= {arXiv preprint arXiv:math/0410069},
year = {2007}
}
Comments
Typos corrected. To appear in Beitrage zur Algebra und Geometrie