Broken circuit complexes and hyperplane arrangements
We study StanleyReisner 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 OrlikTerao 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 OrlikSolomon algebra.
broken circuit complex hyperplane arrangement resolution complete intersection matroid orlikterao algebra