A self-contained geometric proof of the wall-crossing formula via path-lifting rules for spectral networks, including spiral domains, with the charge lattice generated by A0-laminations.
Joyce structures on spaces of quadratic differentials
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abstract
Consider the space parameterising curves of genus g>1 equipped with a quadratic differential with simple zeroes. We use the geometry of isomonodromic deformations to construct a complex hyperkahler structure on the total space of its tangent bundle. This provides non-trivial examples of the Joyce structures recently introduced in relation to Donaldson-Thomas theory.
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Wall-crossing formulas via spectral networks
A self-contained geometric proof of the wall-crossing formula via path-lifting rules for spectral networks, including spiral domains, with the charge lattice generated by A0-laminations.