Symplectic resolutions of the Hilbert squares of ADE surface singularities

Abstract

We study symplectic resolutions of the Hilbert scheme of two points on a surface with one ADE-singularity. We also characterize such singularities by central fibers of their symplectic resolutions. As an application, we show that these singularities are isomorphic to the Slodowy slices which are transversal to the `sub-subregular' orbits in the nilpotent cones of ADE-types.

v4: 36 pages, minor revision

References in corpus (1)

• The Hilbert schemes of points on surfaces with rational double point singularities

Cited by in corpus (1)

• Singularities of Fano varieties of lines on singular cubic fourfolds