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Creators/Authors contains: "Wang, Jidong"

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  1. ; ; (, International Mathematics Research Notices)
    Abstract We give a cohomological interpretation of the Heaviside filtration on the Varchenko–Gelfand ring of a pair $$({\mathcal{A}},{\mathcal{K}})$$, where $${\mathcal{A}}$$ is a real hyperplane arrangement and $${\mathcal{K}}$$ is a convex open subset of the ambient vector space. This builds on work of the first author, who studied the filtration from a purely algebraic perspective, as well as work of Moseley, who gave a cohomological interpretation in the special case where $${\mathcal{K}}$$ is the ambient vector space. We also define the Gelfand–Rybnikov ring of a conditional oriented matroid, which simultaneously generalizes the Gelfand–Rybnikov ring of an oriented matroid and the aforementioned Varchenko–Gelfand ring of a pair. We give purely combinatorial presentations of the ring, its associated graded, and its Rees algebra. 
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