Incidence combinatorics of resolutions (Q1880390)

This paper undertakes the combinatorial abstraction of the construction of models for resolution of singularities. It presents, for arbitrary meet-semilattices, suitable notions of combinatorial ``blowups,'' ``building sets,'' and so forth, thereby giving ``a common abstract framework for the incidence combinatorics occurring in the context of the De Concini-Procesi models of subspace arrangements and resolutions of singularities of toric varieties'' (quoting the paper's abstract).