Joyce structures and their twistor spaces

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.

Published version. To appear in Advances in Mathematics. arXiv admin note: text overlap with arXiv:2303.07061