On the zone of a surface in a hyperplane arrangement

descriptionPublicationkeyboard_double_arrow_right Part of book or chapter of book , Conference object , Article 22 Nov 2005 English Publisher:Springer Science and Business Media LLC

Authors: Boris Aronov; Micha Sharir;

doi: 10.1007/bfb0028245

On the zone of a surface in a hyperplane arrangement

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Abstract

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).

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New York University
United States
Courant Institute of Mathematical Sciences
United States

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