Deep Points of Cluster Algebras

2024/03/22 by James C. Beyer, Beyer, James, Greg Muller +1 · 1 citation
Mathematics · #13F60 #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #Cluster (spacecraft) #Commutative Algebra (math.AC) #Computer network #Computer science #FOS: Mathematics #Quantum Algebra (math.QA) #Random Matrices and Applications

paper · pdf · doi:10.48550/arxiv.2403.15589

published in arXiv (Cornell University) (Cornell University)

openalex publication_date 2024/03/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We initiate a systematic study of the deep points of a cluster algebra; that is, the points in the associated variety which are not in any cluster torus. We describe the deep points of cluster algebras of type A, rank 2, Markov, and unpunctured surface type.

Cited by

• Cluster tori over \mathbbF₂, hexagonal moves on triangulations, and minimal coverings of cluster manifolds

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