Abstract

Joyce structures were introduced by Bridgeland in work relating to Donaldson-Thomas invariants and bear resemblance to Frobenius structures. Inspired by the construction of the A2 Joyce structure, we will use the Bailey-Eastwood characterisation of complex hyper-Kähler metrics to construct Joyce structures on particular moduli spaces of meromorphic quadratic differentials on the Riemann sphere. We will observe that the twistor distribution, which coincides with the span of the isomonodromic flows for a family of 2nd order linear ODE with rational potential, may be obtained as the kernel of a 2-form induced by the intersection forms of an associated family of algebraic curves. Important associated data is simply expressible in terms of periods and intersection products of differential forms that appear in WKB analysis of the equation.