The Orlik-Solomon Algebra and the Bergman Fan of a Matroid

Abstract

Given a matroid $M$ one can define its Orlik-Solomon algebra $OS(M)$ and the Bergman fan ${\Sigma }_0(M)$. On the other hand to any rational polyhedral fan $\Sigma$ one can associate its tropical homology and cohomology groups $\F_\bullet(Σ)$, $\F^\bullet (Σ)$. We will show that the projective Orlik-Solomon algebra $O{S}_0(M)$ is canonically isomorphic to $\F^\bullet (Σ_0(M))$.

arXiv comment7 pages, two figures, journal version

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