Extremal decompositions of tropical varieties and relations with rigidity theory
Algebraic Geometry
2024-03-04 v1 Combinatorics
Metric Geometry
Abstract
Extremality and irreducibility constitute fundamental concepts in mathematics, particularly within tropical geometry. While extremal decomposition is typically computationally hard, this article presents a fast algorithm for identifying the extremal decomposition of tropical varieties with rational balanced weightings. Additionally, we explore connections and applications related to rigidity theory. In particular, we prove that a tropical hypersurface is extremal if and only if it has a unique reciprocal diagram up to homothety.
Keywords
Cite
@article{arxiv.2403.00655,
title = {Extremal decompositions of tropical varieties and relations with rigidity theory},
author = {Farhad Babaee and Sean Dewar and James Maxwell},
journal= {arXiv preprint arXiv:2403.00655},
year = {2024}
}
Comments
30 pages, 12 figures