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Ideals of the cohomology rings of Hilbert schemes and their applications | | Wei-Ping Li
; Zhenbo Qin
; Weiqiang Wang
; | | Date: |
9 Aug 2002 | | Journal: | Trans. AMS, Vol.356 No.1 (2004), p245-265 | | Subject: | Algebraic Geometry; Quantum Algebra MSC-class: 14C05(Primary) 14F25, 17B69(Secondary) | math.AG math.QA | | Abstract: | We study the ideals of the rational cohomology ring of the Hilbert scheme X^{[n]} of n points on a smooth projective surface X. As an application, for a large class of smooth quasi-projective surfaces X, we show that every cup product structure constant of H^*(X^{[n]}) is independent of n; moreover, we obtain two sets of ring generators for the cohomology ring H^*(X^{[n]}). Similar results are established for the Chen-Ruan orbifold cohomology ring of the symmetric product. In particular, we prove a ring isomorphism between H^*(X^{[n]}, C) and H^*_{orb}(X^{[n]}/S_n, C) for a large class of smooth quasi-projective surfaces with numerically trivial canonical class. | | Source: | arXiv, math.AG/0208070 | | Services: | Forum | Review | PDF | Favorites | |
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