Slices to sums of adjoint orbits, the Atiyah-Hitchin manifold, and Hilbert schemes of points

• Autorzy: Roger Bielawski
• Języki publikacji: EN

Abstrakty

EN

We show that the regular Slodowy slice to the sum of two semisimple adjoint orbits of GL(n, ℂ) is isomorphic to the deformation of the D2-singularity if n = 2, the Dancer deformation of the double cover of the Atiyah-Hitchin manifold if n = 3, and to the Atiyah-Hitchin manifold itself if n = 4. For higher n, such slices to the sum of two orbits, each having only two distinct eigenvalues, are either empty or biholomorphic to open subsets of the Hilbert scheme of points on one of the above surfaces. In particular, these open subsets of Hilbert schemes of points carry complete hyperkähler metrics. In the case of the double cover of the Atiyah-Hitchin manifold this metric turns out to be the natural L2-metric on a hyperkähler submanifold of the monopole moduli space.

• Wydawca: De Gruyter Open
• Czasopismo: Complex Manifolds
• Rocznik: 2017
• Tom: 4
• Numer: 1
• Strony: 16-36

Daty

wydano

2017-02-01

otrzymano

2016-12-13

zaakceptowano

2016-12-13

online

2017-02-10

Twórcy

autor

Roger Bielawski

• Institut für Differentialgeometrie, Universität Hannover, Welfengarten 1, D-30167, Hannover

Identyfikatory

DOI

10.1515/coma-2017-0003