La singularité de O'Grady

Manfred Lehn (1) , Christoph Sorger (2)

1 MI - Institut für Mathematik
2 LMJL - Laboratoire de Mathématiques Jean Leray

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).

Domaines: Géométrie algébrique [math.AG]

Manfred Lehn, Christoph Sorger. La singularité de O'Grady. Journal of Algebraic Geometry, 2006, 15 (4), pp.753-770. ⟨hal-00004658v2⟩