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arXiv · 1710.06505

Stability conditions and cluster varieties from quivers of type $A$

Dylan G. L. Allegretti
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Abstract

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.

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Dylan G. L. Allegretti. 2017-10-17. Stability conditions and cluster varieties from quivers of type $A$. https://doi.org/10.1016/j.aim.2018.08.017

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