A Salvetti complex for Toric Arrangements and its fundamental group

TL;DR

This paper introduces a combinatorial model for the complement of complexified toric arrangements using nerves of acyclic categories, extending previous work and providing a finite presentation of its fundamental group.

Contribution

It generalizes existing models for toric arrangements and explicitly computes the fundamental group with a finite presentation.

Findings

Developed a combinatorial model using nerves of acyclic categories.

Extended prior work on thick toric arrangements.

Provided a finite presentation of the 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.