Extremal decompositions of tropical varieties and relations with rigidity theory

Research output: Contribution to journalArticle (Academic Journal)

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.
Original languageEnglish
Number of pages30
JournalarXiv
Publication statusIn preparation - 2024

Structured keywords

  • Pure Mathematics

Keywords

  • tropical varieties
  • infinitesimal rigidity
  • reciprocal diagrams
  • parallel redrawings
  • extremal decomposition
  • Newton polytopes
  • duality

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