Characterization of projective spaces by Seshadri constants

Yuchen Liu; Ziquan Zhuang

doi:10.1007/s00209-017-1941-9

Characterization of projective spaces by Seshadri constants

Algebraic Geometry 2018-10-17 v3

Authors: Yuchen Liu , Ziquan Zhuang

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Abstract

We prove that an $n$ -dimensional complex projective variety is isomorphic to $\mathbb{P}^n$ if the Seshadri constant of the anti-canonical divisor at some smooth point is greater than $n$ . We also classify complex projective varieties with Seshadri constants equal to $n$ .

Keywords

Seshadri constants projective spaces anti-canonical divisor complex projective varieties classification

Cite

@article{arxiv.1607.05743,
  title  = {Characterization of projective spaces by Seshadri constants},
  author = {Yuchen Liu and Ziquan Zhuang},
  journal= {arXiv preprint arXiv:1607.05743},
  year   = {2018}
}

Comments

Minor changes. To appear in Mathematische Zeitschrift

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