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Nonexistence of Levi-degenerate hypersurfaces of constant signature in$CP$^{$n$}

Alla Sargsyan Institute of Mathematics, National Academy of Sciences

Differential Geometry mathscidoc:1701.10009

Arkiv for Matematik, 50, (1), 183-197, 2010.2
Let$M$be a smooth hypersurface of constant signature in$CP$^{$n$},$n$≥3. We prove the regularity foron$M$in bidegree (0,1). As a consequence, we show that there exists no smooth hypersurface in$CP$^{$n$},$n$≥3, whose Levi form has at least two zero-eigenvalues.
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@inproceedings{alla2010nonexistence,
  title={Nonexistence of Levi-degenerate hypersurfaces of constant signature in$CP$^{$n$}},
  author={Alla Sargsyan},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203632140305017},
  booktitle={Arkiv for Matematik},
  volume={50},
  number={1},
  pages={183-197},
  year={2010},
}
Alla Sargsyan. Nonexistence of Levi-degenerate hypersurfaces of constant signature in$CP$^{$n$}. 2010. Vol. 50. In Arkiv for Matematik. pp.183-197. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203632140305017.
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