BGG resolutions via configuration spaces

Abstract

We study the blow-ups of configuration spaces. These spaces have a structure of what we call an Orlik–Solomon manifold; it allows us to compute the intersection cohomology of certain flat connections with logarithmic singularities using some Aomoto type complexes of logarithmic forms. Using this construction we realize geometrically the sl2 Bernstein–Gelfand–Gelfand resolution as an Aomoto complex.