Combinatorics of toric arrangements

Abstract

In this paper we build an Orlik–Solomon model for the canonical gradation of the cohomology algebra with integer coefficients of the complement of a toric arrangement. We give some results on the uniqueness of the representation of arithmetic matroids, in order to discuss how the Orlik–Solomon model depends on the poset of layers. The analysis of discriminantal toric arrangements permits us to isolate certain conditions under which two toric arrangements have di¤eomorphic complements. We also give combinatorial conditions determining whether the cohomology algebra is generated in degree one.