Witten’s top Chern class via cosection localization

Chang, Huai-Liang Hong Kong University of Science and Technology Li, Jun Fudan University and Stanford University LI Wei-Ping Hong Kong University of Science and Technology

mathscidoc:1701.01024

Gold Award Paper in 2017

Invent. Math. , 200, (3), 1015-1063, 2015.6
For a Landau–Ginzburg space ([Cn/G], W), we construct Witten’s top Chern class as an algebraic cycle using cosection localized virtual cycles in the case where all sectors are narrow, verify all axioms of this class, and derive an explicit formula for it in the free case. We prove that this construction is equivalent to the constructions of Polishchuk–Vaintrob, Chiodo, and Fan– Jarvis–Ruan.
cosection localisation, FJRW invariants, Witten's top Chern class, virtual cycle.
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@inproceedings{chang,2015witten’s,
  title={Witten’s top Chern class via cosection localization},
  author={Chang, Huai-Liang, Li, Jun, and LI Wei-Ping},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170118103415799417114},
  booktitle={Invent. Math. },
  volume={200},
  number={3},
  pages={1015-1063},
  year={2015},
}
Chang, Huai-Liang, Li, Jun, and LI Wei-Ping. Witten’s top Chern class via cosection localization. 2015. Vol. 200. In Invent. Math. . pp.1015-1063. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170118103415799417114.
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