Joyce structures on spaces of quadratic differentials

Bridgeland, Tom¹

¹Department of Pure Mathematics, University of Sheffield, Sheffield, United Kingdom

Geometry & topology, Tome 29 (2025) no. 5, pp. 2695-2731

Résumé

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.

Détail

DOI : 10.2140/gt.2025.29.2695

Keywords: moduli spaces, flat connections, Higgs bundles, hyperkahler

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