an:05022772
Zbl 1095.13024
Proudfoot, Nicholas; Speyer, David
A broken circuit ring
EN
Beitr. Algebra Geom. 47, No. 1, 161-166 (2006).
00125664
2006
j
13F55 13D40
Summary: Given a matroid \(M\) represented by a linear subspace \(L\subset{\mathbb C}^n\) (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 \(\text{Spec} R(L)\), as well as a stratification indexed by the flats of \(M\).