Local structure of hyperkaehler singularities in O'Grady's examples
Abstract
We study the local structure of the singularity in the moduli space of sheaves on a K3 surface which has been resolved by K O'Grady in his construction of new examples of hyperkaehler manifolds. In particular, we identify the singularity with the closure of a certain nilpotent orbit in the coadjoint representation of the group $Sp(4)$. We also prove that the moduli spaces for some other sets of numerical parameters do not admit a smooth symplectic resolution of singularities.
- Publication:
-
arXiv Mathematics e-prints
- Pub Date:
- May 2004
- DOI:
- 10.48550/arXiv.math/0405575
- arXiv:
- arXiv:math/0405575
- Bibcode:
- 2004math......5575K
- Keywords:
-
- Mathematics - Algebraic Geometry
- E-Print:
- 28 pages, LaTeX2e. Final version, to appear in MMJ