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. 2000 Math. Subj. Class. 14D20.
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