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A hyperplane arrangement is a set of hyperplanes in a vector space or in a projective space. The complement of the union of these hyperplanes defines an algebraic variety, with interesting geometry and topology.

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Is there a characterization of hyperplane arrangement intersection posets?

Chapters 4 and 8 of Oriented Matroids By Anders Björner, Michel Las Vergnas, Bernd Sturmfels, Neil White, Gunter M. Ziegler reviews the big face lattice of oriented matroids, and when that is realiz …
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