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The Hilb/Sym correspondence for C2: descendents and Fourier-Mukai

Rahul Pandharipande ETH-Zurich Hsian-Hua Tseng Ohio State University

mathscidoc:1907.01004

Mathematische Annalen, 375, 509--540, 2019.10
We study here the crepant resolution correspondence for the torus equivariant descendent Gromov-Witten theories of Hilb(C2) and Sym(C2).The descendent correspondence is obtained from our previous matching of the associated CohFTs by applying Givental's quantization formula to a specific symplectic transformation K. The first result of the paper is an explicit computation of K. Our main result then establishes a fundamental relationship between the Fourier-Mukai equivalence of the associated derived categories (by Bridgeland, King, and Reid) and the symplectic transformation K via Iritani's integral structure. The results use Haiman's Fourier-Mukai calculations and are exactly aligned with Iritani's point of view on crepant resolution.
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@inproceedings{rahul2019the,
  title={The Hilb/Sym correspondence for C2: descendents and Fourier-Mukai},
  author={Rahul Pandharipande, and Hsian-Hua Tseng},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20190702223950160806394},
  booktitle={Mathematische Annalen},
  volume={375},
  pages={509--540},
  year={2019},
}
Rahul Pandharipande, and Hsian-Hua Tseng. The Hilb/Sym correspondence for C2: descendents and Fourier-Mukai. 2019. Vol. 375. In Mathematische Annalen. pp.509--540. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20190702223950160806394.
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