On the zone of a surface in a hyperplane arrangement
Let H be a collection of n hyperplanes in ℝ d , let A denote the arrangement of H, and let σ be a (d - 1)-dimensional algebraic surface of low degree, or the boundary of a convex body in ℝd. The zone of σ in A is the collection of cells of A crossed by σ. We show that the total number of faces bounding the cells of the zone of σ is O(nd−1 log n).
KeywordsConvex Body General Position Algebraic Surface Hyperplane Arrangement Simple Arrangement
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