Stability conditions and cluster varieties from quivers of type A
Stability conditions and cluster varieties from quivers of type A
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DOI：
10.1016/j.aim.2018.08.017
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发表时间：
2018-10-15
影响因子：
1.7
通讯作者：
Allegretti, Dylan G. L.
中科院分区：
文献类型：
--
作者：
Allegretti, Dylan G. L.
我们描述了两个空间之间的关系与潜在的一个空间。第一个是一个复杂的流形参数化Bridgeland稳定性条件的三角范畴，第二个是一个集群品种的自然泊松结构。对于A型箭图，我们构造了从稳定性条件空间到簇的局部双全纯。这个映射的存在性来自于Sibuya在经典常微分方程理论中的结果。(C)2018爱思唯尔公司All rights reserved.
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.