La singularité de O'Grady
Résumé
Let M be the moduli space of semistable sheaves with Mukai vector 2v on an abelian or K3 surface where v is primitive such that =2. We show that the blow-up of the reduced singular locus of M provides a symplectic resolution of singularities. This gives a direct description of O'Grady's resolutions of M_{K3}(2,0,4) and M_{Ab}(2,0,2).