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Noether-Lefschetz conjecture and its generalizations

Li, Zhiyuan Shanghai Mathematics Center

mathscidoc:1703.01004

Gold Award Paper in 2017

Invent.Math., 1-52, 2016.9
We prove the Noether-Lefschetz conjecture on the moduli space of quasi-polarized K3 surfaces. This is deduced as a particular case of a general theorem that states that low degree cohomology classes of arithmetic manifolds of orthogonal type are dual to the classes of special cycles, i.e. sub-arithmetic manifolds of the same type. This allows us to apply our results to the moduli spaces of quasi-polarized K3 surfaces.
Noether-Lefschetz conjecture, special cycles on Shimura variety, Hodge conjecture
[ Download ] [ 2017-03-09 14:39:48 uploaded by zhiyuanli ] [ 1157 downloads ] [ 0 comments ] 
@inproceedings{li,2016noether-lefschetz,
  title={Noether-Lefschetz conjecture and its generalizations},
  author={Li, Zhiyuan},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170309143948768239638},
  booktitle={Invent.Math.},
  pages={1-52},
  year={2016},
}
Li, Zhiyuan. Noether-Lefschetz conjecture and its generalizations. 2016. In Invent.Math.. pp.1-52. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170309143948768239638.
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