Journal of Algebraic Geometry

Author(s): Manfred Lehn; Christoph Sorger
Journal: J. Algebraic Geom. 15 (2006), 753-770.
Posted: May 24, 2006
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Abstract: Let $M_{2v}$ be the moduli space of semistable sheaves with Mukai vector

on an abelian or

surface where

is primitive such that $\langle v,v \rangle=2$ . We show that the blow-up of the reduced singular locus of $M_{2v}$ provides a symplectic resolution of singularities. This provides a direct description of O'Grady's resolutions of $M_{K3}(2,0,4)$ and $M_{Ab}(2,0,2)$ .

Résumé. Soit $M_{2v}$ l'espace de modules des faisceaux semi-stables de vecteur de Mukai

sur une surface

ou abélienne où

est primitif tel que $\langle v,v \rangle=2$ . Nous montrons que l'éclatement de $M_{2v}$ le long de son lieu singulier réduit fournit une résolution symplectique des singularités. Ceci donne une description directe des résolutions de O'Grady de $M_{K3}(2,0,4)$ et $M_{Ab}(2,0,2)$ .

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Manfred Lehn
Affiliation: Institut für Mathematik, Johannes Gutenberg-Universität Mainz, D-55099 Mainz, Germany
Email: lehn@mathematik.uni-mainz.de

Christoph Sorger
Affiliation: Institut Universitaire de France & Laboratoire de Mathématiques Jean Leray (UMR 6629 du CNRS), Université de Nantes, 2, Rue de la Houssinière, BP 92208, F-44322 Nantes Cedex 03, France
Email: christoph.sorger@univ-nantes.fr

PII: S 1056-3911(06)00437-1
Received by editor(s): April 22, 2005
Received by editor(s) in revised form: September 29, 2005 and November 3, 2005
Posted: May 24, 2006

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