Tropical cluster varieties, phylogenetic trees, and generalized associahedra

2026/02/16 by Igor Makhlin · 1 voice
Mathematics · #math.AG #math.CO

paper · pdf

arxiv published 2026/02/16 · arxiv updated 2026/04/16

Abstract

We explicitly describe the tropicalization of a type C cluster variety by identifying it with the space of axially symmetric phylogenetic trees. We also study the signed tropicalizations of this cluster variety, realizing them as subfans of the tropicalization that are dual to either associahedra or cyclohedra.

Citations

• Tropical cluster varieties of type C
• Tropicalizing binary geometries
• Minkowski decompositions for generalized associahedra of acyclic type
• Constructing Fano 3-folds from cluster varieties of rank 2
• Canonical bases for cluster algebras
• The Weil-Petersson form on an acyclic cluster variety
• Non-archimedean amoebas and tropical varieties
• Enumerative tropical algebraic geometry in R2
• The tropical totally positive Grassmannian
• Cluster ensembles, quantization and the dilogarithm
• Cluster ensembles, quantization and the dilogarithm
• Moduli spaces of local systems and higher Teichmuller theory
• The Tropical Grassmannian
• Cluster algebras II: Finite type classification

Discussions

• Tropical cluster varieties, phylogenetic trees, and generalized associahedra https://arxiv.org/abs/2602.14957v1 [bsky, 0 points, 0 comments]

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• Tropical cluster varieties of type C
• Tropicalizing binary geometries
• Tropical Grassmannian and Tropical Linear Varieties from phylogenetic trees
• Cluster Algebras of Type D₄, Tropical Planes, and the Positive Tropical Grassmannian
• Phylogenetics in a warm place: computational aspects of the Tropical Grassmannian