Local structure of hyperkaehler singularities in O'Grady's examples

Details Local structure of hyperkaehler singularities in O'Grady's examples Local structure of hyperkaehler singularities in O'Grady's examples

2004-05-29

arxiv.org/abs/math/0405575v2

Mathematics

Algebraic Geometry

28 pages, LaTeX2e. Final version, to appear in MMJ

Scientific paper

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.

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