Combinatorial generators for the cohomology of toric arrangements (Q6592034)

In the paper the authors give a new combinatorial description of the cohomology generators of the complement of a real complexified toric arrangement. To do so they construct a family of subcomplexes \(\{\mathcal S_L\}_L\) of the toric Salvetti complex \(\mathrm{Sal}(\mathcal A)\) such that each subcomplex has the cohomology of the product of a torus and a hyperplane arrangement complement.\N\NThe authors show that the cohomology of \(\mathrm{Sal}(\mathcal A)\), and therefore of the complement of the toric arrangement, injects into the direct sum of the cohomologies of the subcomplexes. This is used to construct generators for the integral cohomology ring of \(\mathrm{Sal}(\mathcal A)\) in terms of standard generators of the torus cohomologies and Orlik-Solomon algebras.\N\NAlthough the relations between generators are not explicitely given, the authors provide an algorithm which is useful in direct calculations, especially for arrangements of dimension 2.