Inventiones mathematicae

, Volume 164, Issue 3, pp 591–614 | Cite as

Singular symplectic moduli spaces

  • D. Kaledin
  • M. Lehn
  • Ch. 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 space that do not belong to these exceptional cases have singularities in codimension ≥4 they do no admit projective symplectic resolutions.


Modulus Space Exceptional Case Symmetric Product Abelian Surface Ample Divisor 
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Copyright information

© Springer-Verlag 2006

Authors and Affiliations

  1. 1.Independent University of MoscowMoscowRussia
  2. 2.Fachbereich Physik, Mathematik und InformatikJohannes Gutenberg-Universität MainzMainzGermany
  3. 3.Institut Universitaire de France et Laboratoire de Mathématiques Jean Leray, UMR 6629 du CNRSUniversité de NantesNantes Cedex 03France

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