Complex hyperkähler structures defined by Donaldson–Thomas invariants
Tom Bridgeland, Ian A. B. Strachan
Abstract
Abstract The notion of a Joyce structure was introduced in Bridgeland (Geometry from Donaldson–Thomas invariants, preprint arXiv:1912.06504 ) to describe the geometric structure on the space of stability conditions of a $$\hbox {CY}_3$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mtext>CY</mml:mtext> <mml:mn>3</mml:mn> </mml:msub> </mml:math> 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.
Topics & Concepts
Tangent spaceMathematicsManifold (fluid mechanics)Pure mathematicsSpace (punctuation)Complex spaceTangentComplex systemStability (learning theory)PreprintAlgebra over a fieldStructural stabilityComplex manifoldStability conditionsTangent vectorComplex geometryTangent bundleTopology (electrical circuits)Geometry and complex manifoldsGeometric Analysis and Curvature FlowsAlgebraic Geometry and Number Theory