Broken circuit complexes and hyperplane arrangements

Abstract

We study Stanley-Reisner ideals of broken circuit complexes and characterize those ones admitting linear resolutions or being complete intersections. These results will then be used to characterize hyperplane arrangements whose Orlik-Terao ideal has the same properties. As an application, we improve a result of Wilf on upper bounds for the coefficients of the chromatic polynomial of a maximal planar graph. We also show that for a matroid with a complete intersection broken circuit complex, the supersolvability of the matroid is equivalent to the Koszulness of its Orlik-Solomon algebra. © 2013 Springer Science+Business Media New York.