Anthony Henderson (University of Sydney)
Friday 4th August, 12.05-12.55pm, Carslaw 373
Poset homology and the cohomology of real DeConcini-Procesi models
Let A be a finite collection of subspaces in a real vector space V. A beautiful result of Goresky and MacPherson describes the cohomology of the complement V\A in purely combinatorial terms, using the homology of the poset of intersections of elements of A. (This generalizes the work of Orlik and Solomon on complex hyperplane arrangements.) A striking analogue, discovered recently by Eric Rains, describes the cohomology of the associated DeConcini-Procesi model, a smooth compact real variety. I will discuss and compare these two results, and present a new generating-function formula for the Betti numbers of the real DeConcini-Procesi variety of type B.