Abstract: In 1995, de Concini and Procesi investigated certain iterative blowups of affine space along intersections of linear subspaces, their wonderful models, a fundamental example being the Fulton-Macpherson configuration space compactification. In doing so, they developed suitable combinatorics to describe, among other things, the cohomology of the wonderful models.

In 2006, Feichtner and Yuzvinsky constructed smooth toric varieties from de Concini and Procesi's combinatorial data, and found that, for any arrangement of hyperplanes, the cohomology ring of the de Concini-Procesi wonderful model is isomorphic to the Chow ring of their toric variety. Their argument is indirect, via the combinatorics defining the rings in question.

I will outline a toric construction of de Concini and Procesi's wonderful models for hyperplane arrangements. This is an example of Tevelev's notion of a tropical compactification. One advantage is that it provides a geometric explanation of Feichtner and Yuzvinsky's isomorphism.