• Corpus ID: 14396490

Hilbert schemes, Hecke algebras and the Calogero-Sutherland system

@article{Costello2003HilbertSH,
  title={Hilbert schemes, Hecke algebras and the Calogero-Sutherland system},
  author={Kevin J. Costello and Ian Grojnowski},
  journal={arXiv: Algebraic Geometry},
  year={2003}
}
We describe the ring structure of the cohomology of the Hilbert scheme of points for a smooth surface X. When X is C 2 , this was done in [13, 21] by realising this ring as a degeneration of the center of CSn. When the canonical class KX = 0, [14] extended this result by defining an algebra structure on H � ({(x, g) ∈ X n × Sn | gx = x}); the Sn-invariants of this algebra is the desired ring. But when KX 6 0 it seems no such algebra can exist. A completely different approach is needed. Instead… 

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