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Transformation of algebraic Gromov-Witten invariants of three-folds under flops and small extremal transitions, with an appendix from the stringy and the symplectic viewpoint

Chien-Hao Liu Shing-Tung Yau

Algebraic Geometry mathscidoc:1912.43637

arXiv preprint math/0505084, 2005.5
We study how Gromov-Witten invariants of projective 3-folds transform under a standard flop and a small extremal transition in the algebro-geometric setting from the recent development of algebraic relative Gromov-Witten theory and its applications. This gives an algebro-geometric account of Witten's wall-crossing formula for correlation functions of the descendant nonlinear sigma model in adjacent geometric phases of a gauge linear sigma model and of the symplectic approach in an earlier work of An-Min Li and Yongbin Ruan on the same problem. A terse account from the stringy and the symplectic viewpoint is given in the appendix to complement and compare to the discussion in the main text.
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@inproceedings{chien-hao2005transformation,
  title={Transformation of algebraic Gromov-Witten invariants of three-folds under flops and small extremal transitions, with an appendix from the stringy and the symplectic viewpoint},
  author={Chien-Hao Liu, and Shing-Tung Yau},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224204622019783201},
  booktitle={arXiv preprint math/0505084},
  year={2005},
}
Chien-Hao Liu, and Shing-Tung Yau. Transformation of algebraic Gromov-Witten invariants of three-folds under flops and small extremal transitions, with an appendix from the stringy and the symplectic viewpoint. 2005. In arXiv preprint math/0505084. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224204622019783201.
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