# Combinatorics and topology of toric arrangements defined by root systems

### Luca Moci

Université Paris-Diderot Paris 7, France

## Abstract

Given the toric (or toral) arrangement defined by a root system $\Phi$, 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 $\Phi$. 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.

## Cite this article

Luca Moci, Combinatorics and topology of toric arrangements defined by root systems. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 19 (2008), no. 4, pp. 293–308

DOI 10.4171/RLM/526