Complex hyperkähler structures defined by Donaldson-Thomas invariants

Abstract

The notion of a Joyce structure was introduced in arXiv:1912.06504 to describe the geometric structure on the space of stability conditions of a CY3 category naturally encoded by the Donaldson-Thomas invariants. In this paper we show that a Joyce structure on a complex manifold defines a complex hyperkähler structure on the total space of its tangent bundle, and give a characterisation of the resulting hyperkähler metrics in geometric terms.

arXiv comment27 pages

References in corpus (7)

• Four-dimensional wall-crossing via three-dimensional field theory
• Noncommutative Instantons and Twistor Transform
• Riemann-Hilbert problems from Donaldson-Thomas theory
• A Geometry for Multidimensional Integrable Systems
• Stability conditions and Stokes factors
• Holomorphic generating functions for invariants counting coherent sheaves on Calabi-Yau 3-folds
• Dressing operator approach to Moyal algebraic deformation of selfdual gravity

Cited by in corpus (10)

• The Celestial Chiral Algebra of Self-Dual Gravity on Eguchi-Hanson Space
• Null Kähler geometry and isomonodromic deformations
• On the monodromy of the deformed cubic oscillator
• Topological recursion and uncoupled BPS structures II: Voros symbols and the $\tau$-function
• Mock modularity at work, or black holes in a forest
• Resurgence of Refined Topological Strings and Dual Partition Functions
• Resurgence and Riemann-Hilbert problems for elliptic Calabi-Yau threefolds
• Joyce structures on spaces of quadratic differentials
• Special Joyce structures and hyperkähler metrics
• Quantum TBA for refined BPS indices