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Generalized witten genus and vanishing theorems

Qingtao Chen University of Southern California Fei Han National University of Singapore Weiping Zhang Nankai University

Differential Geometry mathscidoc:1609.10217

Journal of Differential Geometry, 88, (1), 1-39, 2011
We construct a generalized Witten genus for spinc manifolds, which takes values in level 1 modular forms with integral Fourier expansion on a class of spinc manifolds called stringc manifolds. We also construct a mod 2 analogue of the Witten genus for 8k+2 dimensional spin manifolds. The Landweber-Stong type vanishing theorems are proven for the generalizedWitten genus and the mod 2 Witten genus on stringc and string (generalized) complete intersections in (product of) complex projective spaces respectively.
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@inproceedings{qingtao2011generalized,
  title={GENERALIZED WITTEN GENUS AND VANISHING THEOREMS},
  author={Qingtao Chen, Fei Han, and Weiping Zhang},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160912073847187152876},
  booktitle={Journal of Differential Geometry},
  volume={88},
  number={1},
  pages={1-39},
  year={2011},
}
Qingtao Chen, Fei Han, and Weiping Zhang. GENERALIZED WITTEN GENUS AND VANISHING THEOREMS. 2011. Vol. 88. In Journal of Differential Geometry. pp.1-39. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160912073847187152876.
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