Joyce structures and their twistor spaces
Copyright policy )Joyce structures and their twistor spaces
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
Hyper-Kähler and quaternionic Kähler geometry, ``special'' geometry, Mathematics - Algebraic Geometry, Twistor methods in differential geometry, twistor spaces, Gromov-Witten invariants, quantum cohomology, Frobenius manifolds, FOS: Mathematics, Twistor theory, double fibrations (complex-analytic aspects), Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants (algebro-geometric aspects), hyper-Kähler structures, Donaldson-Thomas invariants, Algebraic Geometry (math.AG), Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with topology, geometry and differential geometry
Hyper-Kähler and quaternionic Kähler geometry, ``special'' geometry, Mathematics - Algebraic Geometry, Twistor methods in differential geometry, twistor spaces, Gromov-Witten invariants, quantum cohomology, Frobenius manifolds, FOS: Mathematics, Twistor theory, double fibrations (complex-analytic aspects), Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants (algebro-geometric aspects), hyper-Kähler structures, Donaldson-Thomas invariants, Algebraic Geometry (math.AG), Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with topology, geometry and differential geometry
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