Characterization of projective spaces and $\mathbb P^r$-bundles as ample divisors

Jie Liu

doi:10.1017/nmj.2017.31

Characterization of projective spaces and $\mathbb P^r$-bundles as ample divisors

Algebraic Geometry 2017-10-12 v3

Authors: Jie Liu

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Abstract

Let $X$ be a projective manifold of dimension $n$ . Suppose that $T_X$ contains an ample subsheaf. We show that $X$ is isomorphic to $\mathbb{P}^n$ . As an application, we derive the classification of projective manifolds containing a $\mathbb{P}^r$ -bundle as an ample divisor by the recent work of D.~Litt.

Keywords

projective manifold ample subsheaf projective space P^r-bundle ample divisor classification algebraic geometry

Cite

@article{arxiv.1611.05823,
  title  = {Characterization of projective spaces and $\mathbb P^r$-bundles as ample divisors},
  author = {Jie Liu},
  journal= {arXiv preprint arXiv:1611.05823},
  year   = {2017}
}

Comments

13 pages. Final version. To appear on Nagoya Mathematical Journal

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