Joyce structures on spaces of quadratic differentials

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.

Published version. To appear in Geometry and Topology

References in corpus (9)

• Four-dimensional wall-crossing via three-dimensional field theory
• Hyper-K{ä}hler Hierarchies and their twistor theory
• Riemann-Hilbert problems from Donaldson-Thomas theory
• Holomorphic generating functions for invariants counting coherent sheaves on Calabi-Yau 3-folds
• Complex hyperkähler structures defined by Donaldson-Thomas invariants
• Voros symbols as cluster coordinates
• Stability conditions, cluster varieties, and Riemann-Hilbert problems from surfaces
• On the monodromy of the deformed cubic oscillator
• Abelianisation of Logarithmic ${\mathfrak{sl}}_2$-Connections