Characterizations of projective spaces and quadrics by strictly nef bundles

杨晓奎 Morningsider center of Mathematics, Institute of Mathematics, CAS Duo Li Yau Mathematics Science Center

Algebraic Geometry mathscidoc:1609.01006

In this paper, we show that if the tangent bundle of a smooth projective variety is strictly nef, then it is isomorphic to a projective space; if a projective variety $X^n$ $(n>4)$ has strictly nef $\Lambda^2 TX$, then it is isomorphic to $\P^n$ or quadric $\Q^n$. We also prove that on elliptic curves, strictly nef vector bundles are ample, whereas there exist Hermitian flat and strictly nef vector bundles on any smooth curve with genus $g\geq 2$.
strictly nef bundle, projective space, quadrics
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@inproceedings{杨晓奎characterizations,
  title={Characterizations of projective spaces and quadrics by strictly nef bundles},
  author={杨晓奎, and Duo Li},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160922165750734340044},
}
杨晓奎, and Duo Li. Characterizations of projective spaces and quadrics by strictly nef bundles. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160922165750734340044.
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