Abstract
An affine oriented matroid M is a combinatorial abstraction of an affine hyperplane arrangement. From M, Novik, Postnikov and Sturmfels [11] constructed a squarefree monomial ideal OM in a polynomial ring S˜, and got beautiful results. Developing their theory, we will show the following.(1)If S˜/OM is Cohen–Macaulay, then the bounded complex BM (a regular CW complex associated with M) is a contractible homology manifold with boundary. This is closely related to Dong's theorem ([5]), which used to be Zaslavsky's conjecture.(2)We give a characterization of M such that S˜/OM is Cohen–Macaulay, which states that the converse of [11, Corollary 2.6] is essentially true.
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