Transverse Hilbert schemes, bi-Hamiltonian systems, and hyperk\"ahler geometry
Differential Geometry
2020-09-29 v2 Symplectic Geometry
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 hyperk\"ahler manifolds arising from the transverse Hilbert scheme construction, with particular attention paid to the monopole moduli spaces.
Keywords
Cite
@article{arxiv.2001.05669,
title = {Transverse Hilbert schemes, bi-Hamiltonian systems, and hyperk\"ahler geometry},
author = {Roger Bielawski},
journal= {arXiv preprint arXiv:2001.05669},
year = {2020}
}
Comments
14 pages; minor changes in v.2; to appear in the Atiyah Memorial Volume of the Q.J.Math.${}$