Stability scattering diagrams and quiver coverings

2023/06/07 by Qiyue Chen, Chen, Qiyue, Travis Mandel +2 · 1 citation
Mathematics · Physics and Astronomy · #13F60 #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #FOS: Mathematics #General Topology (math.GN) #Geometry and complex manifolds #Quantum many-body systems #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2306.04104

openalex publication_date 2023/06/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Given a covering of a quiver (with potential), we show that the associated Bridgeland stability scattering diagrams are related by a restriction operation under the assumption of admitting a nice grading. We apply this to quivers with potential associated to marked surfaces. In combination with recent results of the second and third authors, our findings imply that the bracelets basis for a once-punctured closed surface coincides with the theta basis for the associated stability scattering diagram, and these stability scattering diagrams agree with the corresponding cluster scattering diagrams of Gross-Hacking-Keel-Kontsevich except in the case of the once-punctured torus.

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