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arXiv · 2303.16467

A complex analogue of the Goodman-Pollack-Wenger theorem

Daniel McGinnis
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Abstract

A \textit{$k$-transversal} to family of sets in $\mathbb{R}^d$ is a $k$-dimensional affine subspace that intersects each set of the family. In 1957 Hadwiger provided a necessary and sufficient condition for a family of pairwise disjoint, planar convex sets to have a $1$-transversal. After a series of three papers among the authors Goodman, Pollack, and Wenger from 1988 to 1990, Hadwiger's Theorem was extended to necessary and sufficient conditions for $(d-1)$-transversals to finite families of convex sets in $\mathbb{R}^d$ with no disjointness condition on the family of sets. We prove an analogue of the Goodman-Pollack-Wenger theorem in the complex setting.

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Daniel McGinnis. 2023-03-29. A complex analogue of the Goodman-Pollack-Wenger theorem. https://arxiv.org/abs/2303.16467

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