Voronoi diagrams of algebraic varieties under polyhedral norms

2022/09/23 by Becedas, Adrian, Kohn, Kathlén, Venturello, Lorenzo
#14N10 #49Q22 #51F99 #Algebraic Geometry (math.AG) #FOS: Mathematics #Metric Geometry (math.MG)

paper · doi:10.48550/arxiv.2209.11463

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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