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arXiv · 1201.3094

The Cohomological Crepant Resolution Conjecture for the Hilbert-Chow morphisms

Wei-Ping Li·Zhenbo Qin
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Abstract

In this paper, we prove that Ruan's Cohomological Crepant Resolution Conjecture holds for the Hilbert-Chow morphisms. There are two main ideas in the proof. The first one is to use the representation theoretic approach proposed in [QW] which involves vertex operator techniques. The second is to prove certain universality structures about the 3-pointed genus-0 extremal Gromov-Witten invariants of the Hilbert schemes by using the indexing techniques from [LiJ], the product formula from [Beh2] and the co-section localization from [KL1, KL2, LL]. We then reduce Ruan's Conjecture from the case of an arbitrary surface to the case of smooth projective toric surfaces which has already been proved in [Che].

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Wei-Ping Li, Zhenbo Qin. 2013-06-07. The Cohomological Crepant Resolution Conjecture for the Hilbert-Chow morphisms. https://arxiv.org/abs/1201.3094

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