Combinatorics and topology of toric arrangements defined by root systems

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<jats:p> Given the toric (or toral) arrangement defined by a root system <jats:inline-formula> <jats:tex-math>\Phi</jats:tex-math> </jats:inline-formula> , we classify and count its components of each dimension. We show how to reduce to the case of 0-dimensional components, and in this case we give an explicit formula involving the maximal subdiagrams of the affine Dynkin diagram of <jats:inline-formula> <jats:tex-math>\Phi</jats:tex-math> </jats:inline-formula> . Then we compute the Euler characteristic and the Poincar\'{e} polynomial of the complement of the arrangement, that is the set of regular points of the torus. </jats:p>

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