Beitr\ EMIS ELibM Electronic Journals Beiträge zur Algebra und Geometrie
Contributions to Algebra and Geometry
Vol. 47, No. 1, pp. 161-166 (2006)

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A broken circuit ring

Nicholas Proudfoot and David Speyer

Department of Mathematics, University of Texas, Austin, TX 78712; Department of Mathematics, University of California, Berkeley, CA 94720

Abstract: 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 $\Spec R(L)$, as well as a stratification indexed by the flats of $M$.

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Electronic version published on: 9 May 2006. This page was last modified: 4 Nov 2009.

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