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Singular symplectic moduli spaces

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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 ≥4 they do no admit projective symplectic resolutions.

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Authors and Affiliations

  1. Independent University of Moscow, B. Vlassievski per. 11, Moscow, 119002, Russia

    D. Kaledin

  2. Fachbereich Physik, Mathematik und Informatik, Johannes Gutenberg-Universität Mainz, 55099, Mainz, Germany

    M. Lehn

  3. Institut Universitaire de France et Laboratoire de Mathématiques Jean Leray, UMR 6629 du CNRS, Université de Nantes, 2, Rue de la Houssinière, BP 92208, 44322, Nantes Cedex 03, France

    Ch. Sorger

Authors
  1. D. Kaledin
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  2. M. Lehn
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  3. Ch. Sorger
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Corresponding authors

Correspondence to D. Kaledin, M. Lehn or Ch. Sorger.

Additional information

A la mémoire de Joseph Le Potier

Mathematics Subject Classification (1991)

14J60, 14D20, 14J28, 32J27

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Kaledin, D., Lehn, M. & Sorger, C. Singular symplectic moduli spaces. Invent. math. 164, 591–614 (2006). https://doi.org/10.1007/s00222-005-0484-6

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  • DOI: https://doi.org/10.1007/s00222-005-0484-6

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