Incidence combinatorics of resolutions

Eva-Maria Feichtner and Dmitry N. Kozlov

To appear at Formal Power Series and Algebraic Combinatorics (FPSAC01), Tempe, Arizona (USA), May 20-26, 2001


For an arbitrary meet-semilattice we introduce notions of combinatorial blowups, building sets, and nested sets. This gives a common abstract framework for the incidence combinatorics occurring in the context of DeConcini-Procesi models of subspace arrangements and resolutions of singularities in toric varieties. Our main theorem states that a sequence of combinatorial blowups, prescribed by a building set in linear extension compatible order, gives the face poset of the simplicial complex of nested sets. As applications we trace the incidence combinatorics through every step of the DeConcini-Procesi model construction, and we introduce the notions of building sets and nested sets to the context of toric varieties.

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