English

Voronoi diagrams of algebraic varieties under polyhedral norms

Algebraic Geometry 2022-09-26 v1 Metric Geometry

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.

Keywords

Cite

@article{arxiv.2209.11463,
  title  = {Voronoi diagrams of algebraic varieties under polyhedral norms},
  author = {Adrian Becedas and Kathlén Kohn and Lorenzo Venturello},
  journal= {arXiv preprint arXiv:2209.11463},
  year   = {2022}
}