Complex hyperk\"ahler 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 hyperk\"ahler structure on the total space of its tangent bundle, and give a characterisation of the resulting hyperk\"ahler metrics in geometric terms.