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arXiv · 2412.00551

How to stab a polytope

Sebastian Seemann·Francesca Zaffalon
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Abstract

We study the set of linear subspaces of a fixed dimension intersecting a given polytope. To describe this set as a semialgebraic subset of a Grassmannian, we introduce a Schubert arrangement of the polytope, defined by the Chow forms of the polytope's faces of complementary dimension. We show that the set of subspaces intersecting a specified family of faces is defined by fixing the sign of the Chow forms of their boundaries. We give inequalities defining the set of stabbing subspaces in terms of sign conditions on the Chow form.

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Sebastian Seemann, Francesca Zaffalon. 2024-11-30. How to stab a polytope. https://arxiv.org/abs/2412.00551

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