Singular symplectic moduli spaces
By D. Kaledin, M. Lehn, Christoph Sorger. 2005
65 citations recorded by the source corpus.
Moduli spaces of semistable sheaves on a K3 or abelian surface with respect to a general ample divisor are shown to be locally factorial, with the exception of symmetric products of a K3 or abelian surface and the class of moduli spaces found by O’Grady. Consequently, since singular moduli space that do not belong to these exceptional cases have singularities in codimension ≥4 they do no admit projective symplectic resolutions.
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/6c0528736e2f0b411944e9a0d3c54c2ee449a5fc
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In Geometry and Topology
- Chunyi Li
- Emanuele Macrì
- Xiaolei Zhao
- Arend Bayer
- Benjamin Schmidt
- Kieran G. O’Grady
- P. Stellari
- D. Huybrechts
In Mathematical Physics
- Chunyi Li
- Emanuele Macrì
- Arend Bayer
- Xiaolei Zhao
- Kieran G. O’Grady
- Yukinobu Toda
- D. Huybrechts
- P. Stellari
Citations in the corpus
- Moduli of sheaves and the Chow group of K3 surfaces (2012, methodology): “K Mst v (X,H) (4.0.14) which is generically injective (recall that with the above hypotheses h0(F) = 1 for the generic F fitting into Extension (4.0.5)). The moduli space Mst v (X,H) is irreducible by [7]; since dimX[n] = 2n = 2+v2 = dimMst v (X,H) (4.0.15) it follows that (4.0.14) is a birational ma”
- MMP for moduli of sheaves on K3s via wall-crossing: nef and movable cones, Lagrangian fibrations (2013, result): “ resolution f: M˜ → M, the pull-back ofωto f−1(Mreg) extends to a holomorphic form on M˜. Our results in [BM12] reduce the following theorem to the case of moduli of sheaves: Theorem 3.8 ([O’G99] and [KLS06]). Let (X,α) be a twisted K3 surface and let v = mv0 ∈ H∗ alg(X,α,Z) be a Mukai vector with v”
- Birational models of moduli spaces of coherent sheaves on the projective plane (2016, background): “The only necessary change is to the formula at the bottom of page 608 of [22].”