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Bibliographic Details
Main Authors: Neville, Scott, Simental, José
Format: Preprint
Published: 2026
Subjects:
Online Access:https://arxiv.org/abs/2603.17890
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Table of Contents:
  • The deep locus of a cluster variety is defined to be the set of its points that do not belong to any cluster torus. We show that, if the cluster variety has a seed whose mutable part is a tree without multiple edges, then the deep locus can be characterized as the set of points whose stabilizer under a certain group action is nontrivial. Deep points without a stabilizer are called mysterious. We establish that many other classes of acyclic quivers (including keys) often have mysterious points. This refutes Conjecture 1.1 of arXiv:2402.16970, but establishes it in many important cases.