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Mukai flop and Ruan cohomology

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Abstract.

Suppose that two compact symplectic manifolds X,X′ are connected by a sequence of simple Mukai flops. In this paper, we construct a ring isomorphism between cohomology rings of X and X′. Using the localization technique, we prove that the quantum corrected products on X,X′ are the ordinary intersection products. Furthermore, X,X′ have isomorphic Ruan cohomology, i.e. we verify the cohomological minimal model conjecture proposed by Ruan for the pair (X,X′).

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Authors and Affiliations

  1. Department of Mathematics, Zhongshan University, Guangzhou, 510275, P.R. China

    Jianxun Hu

  2. Department of Mathematics, University of Wisconsin-Madison, Madison, WI, 53706, USA

    Wanchuan Zhang

Authors
  1. Jianxun Hu
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  2. Wanchuan Zhang
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Correspondence to Jianxun Hu.

Additional information

Mathematics Subject Classification (2001): 14N35, 53D45

Supported in part by NSF of China (10171114 and 10231050).

Revised version: 9 April 2004

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Hu, J., Zhang, W. Mukai flop and Ruan cohomology. Math. Ann. 330, 577–599 (2004). https://doi.org/10.1007/s00208-004-0561-y

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  • DOI: https://doi.org/10.1007/s00208-004-0561-y

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