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arXiv · 1405.7822

Algebraic Boundaries of Convex Semi-algebraic Sets

Rainer Sinn
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Abstract

We study the algebraic boundary of a convex semi-algebraic set via duality in convex and algebraic geometry. We generalize the correspondence of facets of a polytope to the vertices of the dual polytope to general semi-algebraic convex bodies. In the general setup, exceptional families of extreme points might exist and we characterize them semi-algebraically. We also give an algorithm to compute a complete list of exceptional families, given the algebraic boundary of the dual convex set.

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Rainer Sinn. 2014-05-30. Algebraic Boundaries of Convex Semi-algebraic Sets. https://arxiv.org/abs/1405.7822

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