Joyce structures on spaces of quadratic differentials
Tom Bridgeland
TL;DR
This paper constructs complex hyperkahler structures on spaces of quadratic differentials using isomonodromic deformations, providing new examples of Joyce structures linked to Donaldson-Thomas theory.
Contribution
It introduces a novel geometric construction of Joyce structures on moduli spaces of quadratic differentials via isomonodromic deformations.
Findings
Constructed complex hyperkahler structures on quadratic differential spaces
Provided new examples of Joyce structures in Donaldson-Thomas theory
Linked geometric structures to isomonodromic deformation theory
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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Taxonomy
TopicsMathematical and Theoretical Analysis · Advanced Topology and Set Theory · advanced mathematical theories