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 M_v of H-semistable sheaves on S whose Mukai vector is v admits a symplectic resolution \widetilde{M}_v. A particular case is the 10-dimensional O'Grady example \widetilde{M}_10 of an irreducible symplectic manifold. We show that \widetilde{M}_v is an irreducible symplectic manifold which is deformation equivalent to \widetilde{M}_10 and that H2(M_v,\mathbb{Z}) is Hodge isometric to the sublattice v^{\perp} of the Mukai lattice of S. Similar results are shown when S is an abelian surface. Â© Walter de Gruyter Berlin Â· Boston 2013.

Deformation of the O'Grady moduli spaces

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 M_v of H-semistable sheaves on S whose Mukai vector is v admits a symplectic resolution \widetilde{M}_v. A particular case is the 10-dimensional O'Grady example \widetilde{M}_10 of an irreducible symplectic manifold. We show that \widetilde{M}_v is an irreducible symplectic manifold which is deformation equivalent to \widetilde{M}_10 and that H2(M_v,\mathbb{Z}) is Hodge isometric to the sublattice v^{\perp} of the Mukai lattice of S. Similar results are shown when S is an abelian surface. Â© Walter de Gruyter Berlin Â· Boston 2013.
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2013
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Utilizza questo identificativo per citare o creare un link a questo documento: `https://hdl.handle.net/11567/896989`
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