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 (M) over tilde (v). A particular case is the 10-dimensional O'Grady example (M) over tilde (10) of an irreducible symplectic manifold. We show that (M) over tilde (v) is an irreducible symplectic manifold which is deformation equivalent to (M) over tilde (10) and that H-2 (M-v, Z) is Hodge isometric to the sublattice v(perpendicular to) of the Mukai lattice of S. Similar results are shown when S is an abelian surface.

Perego, A., Rapagnetta, A. (2013). Deformation of the O'Grady moduli spaces. JOURNAL FÜR DIE REINE UND ANGEWANDTE MATHEMATIK, 678, 1-34 [10.1515/CRELLE.2011.191].

Deformation of the O'Grady moduli spaces

RAPAGNETTA, ANTONIO
2013-01-01

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 (M) over tilde (v). A particular case is the 10-dimensional O'Grady example (M) over tilde (10) of an irreducible symplectic manifold. We show that (M) over tilde (v) is an irreducible symplectic manifold which is deformation equivalent to (M) over tilde (10) and that H-2 (M-v, Z) is Hodge isometric to the sublattice v(perpendicular to) of the Mukai lattice of S. Similar results are shown when S is an abelian surface.
2013
Pubblicato
Rilevanza internazionale
Articolo
Esperti anonimi
Settore MAT/03 - GEOMETRIA
English
Perego, A., Rapagnetta, A. (2013). Deformation of the O'Grady moduli spaces. JOURNAL FÜR DIE REINE UND ANGEWANDTE MATHEMATIK, 678, 1-34 [10.1515/CRELLE.2011.191].
Perego, A; Rapagnetta, A
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2108/89982
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