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arXiv · 2607.08494

Orlik--Solomon sheaf homology of geometric lattices

Ye Liu
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Abstract

We associate the Orlik--Solomon sheaf with a finite geometric lattice and compute its sheaf homology. We show that this homology concentrates in top degree, admitting a convolution-type decomposition into a principal ideal OS piece tensoring with a principal filter complement poset homology. Applications to uniform matroids provide interesting representations of symmetric groups.

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Ye Liu. 2026-07-09. Orlik--Solomon sheaf homology of geometric lattices. https://arxiv.org/abs/2607.08494

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