Abstract
Abstract
We describe a family of compactifications of the space of Bridgeland stability conditions of a triangulated category, following earlier work by Bapat, Deopurkar and Licata. We particularly consider the case of the 2-Calabi–Yau category of the
$A_2$
quiver. The compactification is the closure of an embedding (depending on q) of the stability space into an infinite-dimensional projective space. In the
$A_2$
case, the three-strand braid group
$B_3$
acts on this closure. We describe two distinguished braid group orbits in the boundary, points of which can be identified with certain rational functions in q. Points in one of the orbits are exactly the q-deformed rational numbers recently introduced by Morier-Genoud and Ovsienko, while the other orbit gives a new q-deformation of the rational numbers. Specialising q to a positive real number, we obtain a complete description of the boundary of the compactification.
Publisher
Cambridge University Press (CUP)
Subject
Computational Mathematics,Discrete Mathematics and Combinatorics,Geometry and Topology,Mathematical Physics,Statistics and Probability,Algebra and Number Theory,Theoretical Computer Science,Analysis
Reference18 articles.
1. [2] Bapat, A. , Deopurkar, A. , and Licata, A. M. . A Thurston compactification of the space of stability conditions, 2020. https://arxiv.org/abs/2011.07908.
2. Spherical objects and stability conditions on 2-Calabi–Yau quiver categories
3. Braid group actions on derived categories of coherent sheaves
4. [6] Heng, E. . Categorification and dynamics in generalised braid groups, 2022. URL https://doi-org.virtual.anu.edu.au/10.1007/BF01357141. PhD Thesis.
5. q-Deformations in the modular group and of the real quadratic irrational numbers
Cited by
4 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献