Joyce structures and their twistor spaces

TL;DR

This paper introduces Joyce structures, explores their twistor spaces, and presents new mathematical results, linking complex hyperkahler geometry with Donaldson-Thomas invariants.

Contribution

It provides a detailed introduction to Joyce structures and proves several new results about their twistor spaces.

Findings

New insights into the geometry of Joyce structures

Development of the theory of their twistor spaces

Establishment of novel mathematical results

Abstract

Joyce structures are a class of geometric structures which first arose in relation to holomorphic generating functions for Donaldson-Thomas invariants. They can be thought of as non-linear analogues of Frobenius structures, or as special classes of complex hyperkahler manifolds. We give a detailed introduction to Joyce structures, with particular focus on the geometry of the associated twistor space. We also prove several new results.