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arXiv · 0912.5458

Combinatorics and topology of toric arrangements defined by root systems

Luca Moci
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Abstract

Given the toric (or toral) arrangement defined by a root system $Φ$, we describe the poset of its layers (connected components of intersections) and we count its elements. Indeed we show how to reduce to zero-dimensional layers, and in this case we provide an explicit formula involving the maximal subdiagrams of the affine Dynkin diagram of $Φ$. Then we compute the Euler characteristic and the Poincare' polynomial of the complement of the arrangement, which is the set of regular points of the torus.

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Luca Moci. 2009-12-30. Combinatorics and topology of toric arrangements defined by root systems. https://arxiv.org/abs/0912.5458

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