Wonderful models for toric arrangements

TL;DR

This paper constructs a smooth geometric model for toric arrangements using a novel combinatorial approach, providing detailed descriptions of its structure and properties.

Contribution

It introduces a toric analog of nested set combinatorics to build and analyze a wonderful model for toric arrangements.

Findings

The model is proven to be smooth.

A detailed geometric description of the normal crossing divisor is provided.

The combinatorial framework for the model is established.

Abstract

We build a wonderful model for toric arrangements. We develop the "toric analog" of the combinatorics of nested sets, which allows to define a family of smooth open sets covering the model. In this way we prove that the model is smooth, and we give a precise geometric and combinatorial description of the normal crossing divisor.