Deformation of the OGrady moduli spacesReportar como inadecuado

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1 Géométrie IECL - Institut Élie Cartan de Lorraine 2 Università degli Studi di Roma Tor Vergata Roma

Abstract : In this paper we study moduli spaces of sheaves on an abelian or projective K3 surface. If S is a K3, v = 2w is a Mukai vector on S, where w is primitive and w 2 = 2, and H is a v−generic polarization on S, then the moduli space Mv of H−semistable sheaves on S whose Mukai vector is v admits a symplectic resolution Mv. A particular case is the 10−dimensional O-Grady example M10 of irreducible symplectic manifold. We show that Mv is an irreducible symplectic manifold which is deformation equivalent to M10 and that H 2 Mv, Z is Hodge isometric to the sublattice v ⊥ of the Mukai lattice of S. Similar results are shown when S is an abelian surface.

Keywords : Moduli spaces of sheaves K3 surfaces abelian surfaces symplectic resolutions deformations

Autor: Arvid Perego - Antonio Rapagnetta -



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