Singular symplectic moduli spaces

Dmitry Kaledin (1) , Manfred Lehn (2) , Christoph Sorger (3)

1 IUM - Independent University of Moscow
2 MI - Fachbereich für Mathematik und Informatik
3 LMJL - Laboratoire de Mathématiques Jean Leray

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 space that do not belong to these exceptional cases have singularities in codimension $\geq4$ they do no admit projective symplectic resolutions.

Domaines: Géométrie algébrique [math.AG]

Dmitry Kaledin, Manfred Lehn, Christoph Sorger. Singular symplectic moduli spaces. Inventiones Mathematicae, 2006, 164 (3), pp.591-614. ⟨10.1007/s00222-005-0484-6⟩. ⟨hal-00004660⟩