Broken circuit complexes and hyperplane arrangements

Abstract

We study Stanley-Reisner ideals of broken circuits complexes and characterize those ones admitting a linear resolution or being complete intersections. These results will then be used to characterize 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 an ordered matroid with disjoint minimal broken circuits, the supersolvability of the matroid is equivalent to the Koszulness of its Orlik-Solomon algebra.

21 pages

References in corpus (1)

• Modular decomposition of the Orlik-Terao algebra of a hyperplane arrangement

Cited by in corpus (5)

• Flawlessness of $h$-vectors of broken circuit complexes
• Koszulness and supersolvability for Dirichlet arrangements
• The Orlik-Terao algebra and the cohomology of configuration space
• Broken circuit complexes of series-parallel networks
• On the Gorensteinness of broken circuit complexes and Orlik--Terao ideals