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Joyce structures on spaces of quadratic differentials

Tom Bridgeland
Geometry & Topology 29 (2025) 2695–2731
DOI: 10.2140/gt.2025.29.2695
Abstract

Consider the space parametrising complex projective curves of genus g equipped with a quadratic differential with simple zeroes. We use the geometry of isomonodromic deformations to construct a complex hyperkähler structure on the total space of its tangent bundle. This provides nontrivial examples of the Joyce structures introduced by the author in relation to Donaldson–Thomas theory.

Keywords
moduli spaces, flat connections, Higgs bundles, hyperkahler
Mathematical Subject Classification
Primary: 14H60, 14H70
References
Publication
Received: 17 April 2024
Revised: 7 October 2024
Accepted: 16 November 2024
Published: 14 August 2025
Proposed: Mark Gross
Seconded: Simon Donaldson, Arend Bayer
Authors
Tom Bridgeland
Department of Pure Mathematics
University of Sheffield
Sheffield
United Kingdom
© 2025 The Author(s), under exclusive license to MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY).

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