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 \(\hbox {CY}_3\) 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.

中文翻译：

---

由Donaldson–Thomas不变量定义的复杂hyperkähler结构

乔伊斯（Joyce）结构的概念是在Bridgeland（唐纳森-托马斯不变式的几何，预印本arXiv：1912.06504）中引入的，用于描述由自然编码的\（\ hbox {CY} _3 \）类别的稳定性条件空间上的几何结构。Donaldson-Thomas不变量。在本文中，我们证明了在复流形上的Joyce结构在其切线束的总空间上定义了一个复hyperkähler结构，并以几何形式给出了所得hyperkähler度量的表征。