Flops, motives and invariance of quantum rings

Yuan-Pin Lee Department of Mathematics, University of Utah, Salt Lake City, Utah, 84112 Hui-Wen Lin Department of Mathematics, National Taiwan University, Taipei 106 Chin-Lung Wang Department of Mathematics, National Taiwan University, Taipei 106

Algebraic Geometry mathscidoc:2204.45018

2006.8
For ordinary flops, the correspondence defined by the graph closure is shown to give equivalence of Chow motives and to preserve the Poincaré pairing. In the case of simple ordinary flops, this correspondence preserves the big quantum cohomology ring after an analytic continuation over the extended Kähler moduli space. For Mukai flops, it is shown that the birational map for the local models is deformation equivalent to isomorphisms. This implies that the birational map induces isomorphisms on the full quantum rings and all the quantum corrections attached to the extremal ray vanish.
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@inproceedings{yuan-pin2006flops,,
  title={Flops, motives and invariance of quantum rings},
  author={Yuan-Pin Lee, Hui-Wen Lin, and Chin-Lung Wang},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220415113455488247036},
  year={2006},
}
Yuan-Pin Lee, Hui-Wen Lin, and Chin-Lung Wang. Flops, motives and invariance of quantum rings. 2006. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220415113455488247036.
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