Published in Journal of Gökova Geometry Topology, Volume 7 (2013)
Title The Orlik-Solomon algebra and the Bergman fan of a Matroid
Author Ilia Zharkov
Given a matroid M one can define its Orlik-Solomon algebra OS(M) and the Bergman fan Σ0(M). On the other hand to any rational polyhedral fan Σ one can associate its tropical homology and cohomology groups F(Σ), F(Σ). We show that the projective Orlik-Solomon algebra OS0(M) is canonically isomorphic to F0(M)). In the realizable case this provides a geometric interpretation of the homology of the complement of the corresponding hyperplane arrangement in Pn.
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Submitted: Mar 4, 2013
Accepted: Aug 28, 2013
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