La singularité de O’Grady

By M. Lehn, C. Sorger. 2005

77 citations recorded by the source corpus.

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).

Subfields: Geometry and Topology, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/171ca088dc3d4345e41d938ba316f131f4f34210

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Geometry and Topology

1. M. Shen
2. Charles Vial
3. A. Perego
4. A. Rapagnetta
5. Giovanni Mongardi
6. L. Fu
7. Robert Laterveer

In Statistical and Nonlinear Physics

1. M. Shen
2. A. Rapagnetta
3. Robert Laterveer
4. Giovanni Mongardi
5. A. Perego
6. Charles Vial
7. L. Fu

Citations in the corpus

• Deformation of the O'Grady moduli spaces (2010, methodology): “Nt 1⁄4 MwtðXt;HtÞ for every t A T : by [11], for every t A T we have that St F Sym (2)ðMwtÞ, hence fjS : S ! T is identified with the morphism j : Sym(2) TðNÞ ! T induced by j.”
• On the Beauville form of the known irreducible symplectic varieties (2006, background): “Since by [10] the smooth variety M10 is the blow up of M(2,0,−2) along , and 0 is a Cartier divisor of B0, it follows that B̃0 is isomorphic to B0 and the intersection ̃ ∩ B̃0 is the exceptional divisor of the blow up of B0 along 0.”
• The generalized Franchetta conjecture for some hyper-Kähler varieties, II (2020, methodology): “…of moduli spaces of H -semistable sheaves with such a Mukai vector v on a K3 or abelian surface with the polarization H being v -generic, such a crepant resolution was constructed first by O’Grady [O’G99] for some special v , and then by Lehn–Sorger [LS06] and Perego–Rapagnetta [PR13] in general.”
• Monodromy and birational geometry of O'Grady's sixfolds (2019, background): “Later M. 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, alon”