Deformation of the O'Grady moduli spaces

By A. Perego, A. Rapagnetta. 2010

50 citations recorded by the source corpus.

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 w2 = 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 M̃v. A particular case is the 10-dimensional O'Grady example M̃10 of an irreducible symplectic manifold. We show that M̃v is an irreducible symplectic manifold which is deformation equivalent to M̃10 and that H2(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.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/caf06ac81b9bea618482777cef7f87a74d55562c

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In Geometry and Topology

1. A. Rapagnetta
2. Giovanni Mongardi
3. A. Perego
4. M. Shen
5. Charles Vial

In Mathematical Physics

1. Giovanni Mongardi
2. A. Rapagnetta
3. A. Perego
4. M. Shen
5. Charles Vial

Citations in the corpus

• Monodromy and birational geometry of O'Grady's sixfolds (2019, background): “Lehn and Sorger [15] showed that, under our assumption on w, the blow up of the Albanese fibre of the moduli space along its singular locus always gives a crepant resolution and Perego and the second named author proved in [34] that these crepant resolutions are deformation equivalent, along smooth ”