Stability conditions, cluster varieties, and Riemann-Hilbert problems from surfaces
Algebraic Geometry
2021-01-29 v3 High Energy Physics - Theory
Geometric Topology
Abstract
We consider two interesting spaces associated to a quiver with potential: a space of stability conditions and a cluster variety. In the case where the quiver with potential arises from an ideal triangulation of a marked bordered surface, we construct a natural map from a dense subset of the space of stability conditions to the cluster variety. Using this construction, we give solutions to a family of Riemann-Hilbert problems arising in Donaldson-Thomas theory.
Cite
@article{arxiv.1912.05938,
title = {Stability conditions, cluster varieties, and Riemann-Hilbert problems from surfaces},
author = {Dylan G. L. Allegretti},
journal= {arXiv preprint arXiv:1912.05938},
year = {2021}
}
Comments
57 pages. Version 2: Some definitions reworded prior to journal submission. Version 3: Incorporated suggestions from referee