On projective wonderful models for toric arrangements and their cohomology

This paper is divided into two parts. The first part is a brief survey, accompanied by concrete examples, on the main results of the papers (De Concini and Gaiffi in Adv Math 327:390–09, 2018; Algebr Geom Topol 19(1):503–532, 2019): the construction of projective models of toric arrangements and the presentation of their cohomology rings by generators and relations. In the second part we focus on the notion of well-connected building set that appears in the cohomological computations mentioned above: we explore some of its properties in the more general context of arrangements of subvarieties of a variety X.