Singular symplectic moduli spaces
by
Manfred Lehn
Johannes Gutenberg Universität Mainz
Coauthors: Dmitry Kaledin, Christoph Sorger

Moduli spaces of semistable sheaves on a K3 or abelian surface with respect to a general ample divisor are shown to be locally factorial, with the exception of symmetric products of a K3 or abelian surface and the class of moduli spaces found by O'Grady. Consequently, since singular moduli spaces that do not belong to these exceptional cases have singularities in codimension ³ 4 they do not admit projective symplectic resolutions.

Paper reference: arXiv:math.AG/0504202