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arXiv · 1912.05938

Stability conditions, cluster varieties, and Riemann-Hilbert problems from surfaces

Dylan G. L. Allegretti
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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.

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Dylan G. L. Allegretti. 2019-12-11. Stability conditions, cluster varieties, and Riemann-Hilbert problems from surfaces. https://doi.org/10.1016/j.aim.2021.107610

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