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Invariance of Quantum Rings under Ordinary Flops II: A quantum Leray--Hirsch theorem

Yuan-Pin Lee Department of Mathematics, University of Utah, Salt Lake City, Utah, 84112 Hui-Wen Lin Taida Institute of Mathematical Sciences (TIMS), National Taiwan University, Taipei 106 Chin-Lung Wang Center for Advanced Study in Theoretical Sciences, National Taiwan University, Taipei 106

Algebraic Geometry mathscidoc:2204.45010

2013.11
This is the second of a sequence of papers proving the quantum invariance for ordinary flops over an arbitrary smooth base. In this paper, we complete the proof of the invariance of the big quantum rings under ordinary flops of splitting type. To achieve that, several new ingredients are introduced. One is a quantum Leray--Hirsch theorem for the local model (a certain toric bundle) which extends the quantum D module of Dubrovin connection on the base by a Picard--Fuchs system of the toric fibers. Nonsplit flops as well as further applications of the quantum Leray--Hirsch theorem will be discussed in subsequent papers. In particular, a quantum splitting principle is developed in Part III which reduces the general ordinary flops to the split case solved here.
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@inproceedings{yuan-pin2013invariance,
  title={Invariance of Quantum Rings under Ordinary Flops II: A quantum Leray--Hirsch theorem},
  author={Yuan-Pin Lee, Hui-Wen Lin, and Chin-Lung Wang},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220415111501373457028},
  year={2013},
}
Yuan-Pin Lee, Hui-Wen Lin, and Chin-Lung Wang. Invariance of Quantum Rings under Ordinary Flops II: A quantum Leray--Hirsch theorem. 2013. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220415111501373457028.
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