Transverse Hilbert schemes, bi-Hamiltonian systems, and hyperkähler geometry

2020/01/16 by Bielawski, Roger
#Differential Geometry (math.DG) #FOS: Mathematics #Symplectic Geometry (math.SG)

paper · doi:10.48550/arxiv.2001.05669

Abstract

We give a characterisation of Atiyah's and Hitchin's transverse Hilbert schemes of points on a symplectic surface in terms of bi-Poisson structures. Furthermore, we describe the geometry of hyperkähler manifolds arising from the transverse Hilbert scheme construction, with particular attention paid to the monopole moduli spaces.

Related

• Holonomic Poisson geometry of Hilbert schemes
• Prop profile of bi-Hamiltonian structures
• Birational geometry of Beauville-Mukai systems III: asymptotic behavior
• Hypertoric varieties, W-Hilbert schemes, and Coulomb branches
• Homogeneous bi-Hamiltonian structures and integrable contact systems