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BGG resolutions via configuration spaces

Michael Falk, Vadim Schechtman, Alexander Varchenko (2014)

Journal de l’École polytechnique — Mathématiques

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 𝔰𝔩 2 Bernstein–Gelfand–Gelfand resolution as an Aomoto complex.

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