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Singular symplectic moduli spaces

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arxiv math/0504202 v1 pith:VNWUZC32 submitted 2005-04-10 math.AG

Dmitry Kaledin (IUM) , Manfred Lehn (MI) , Christoph Sorger (LMJL) This is my paper · ORCID
classification math.AG
keywords modulispacesabeliansingularsurfacesymplecticadmitample
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abstract

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.

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  1. Proper moduli spaces of orthosymplectic complexes

    math.AG 2025-12 conditional novelty 7.0 of 10

    Semistable orthosymplectic complexes on smooth projective varieties admit proper good moduli spaces, giving a new compactification for O_n and Sp_{2n} principal bundle moduli.

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