Voronoi diagrams of algebraic varieties under polyhedral norms
Adrian Becedas, Kathl\'en Kohn, Lorenzo Venturello

TL;DR
This paper investigates Voronoi diagrams of algebraic varieties under polyhedral norms, providing bounds on cell dimensions and counting full-dimensional cells, with applications to polyhedral Wasserstein distances.
Contribution
It introduces bounds on Voronoi cell dimensions and counts full-dimensional cells for algebraic varieties under polyhedral norms, advancing geometric understanding.
Findings
Bounds on Voronoi cell dimensions established
Number of full-dimensional cells counted for algebraic varieties
Application to polyhedral Wasserstein distance analyzed
Abstract
We study Voronoi diagrams of manifolds and varieties with respect to polyhedral norms. We provide upper and lower bounds on the dimensions of Voronoi cells. For algebraic varieties, we count their full-dimensional Voronoi cells. As an application, we consider the polyhedral Wasserstein distance between discrete probability distributions.
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Taxonomy
TopicsCommutative Algebra and Its Applications · Topological and Geometric Data Analysis · Advanced Combinatorial Mathematics
