Stability conditions and cluster varieties from quivers of type A

被引：6
作者：
Allegretti, Dylan G. L.
机构：
来源：
ADVANCES IN MATHEMATICS | 2018年 / 337卷
基金：
欧盟地平线“2020”;
关键词：
Stability condition; Cluster variety; Quadratic differential; Monodronriy data; WKB analysis; POTENTIALS; CATEGORIES; MUTATIONS; ALGEBRAS; SYSTEMS;
D O I：
10.1016/j.aim.2018.08.017
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We describe the relationship between two spaces associated to a quiver with potential. The first is a complex manifold parametrizing Bridgeland stability conditions on a triangulated category, and the second is a cluster variety with a natural Poisson structure. For quivers of type A, we construct a local biholomorphism from the space of stability conditions to the cluster variety. The existence of this map follows from results of Sibuya in the classical theory of ordinary differential equations. (C) 2018 Elsevier Inc. All rights reserved.
引用
收藏
页码：260 / 293
页数：34
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