A Salvetti complex for Toric Arrangements and its fundamental group

Abstract

We describe a combinatorial model for the complement of a complexified toric arrangement by using nerves of acyclic categories. This generalizes recent work of Moci and Settepanella on thick toric arrangements. Moreover, we compute its fundamental group by finding a (finite) presentation.

arXiv comment31 pages, 2/3 figures added, Section 4 updated to address a flaw pointed out by Prof. Salvetti, whom we thank