Very ampleness of the bicanonical line bundle on compact complex two ball quotients

Sai-Kee Yeung

Very ampleness of the bicanonical line bundle on compact complex two ball quotients

Algebraic Geometry 2018-01-10 v3

Authors: Sai-Kee Yeung

Abstract

The purpose of this note is to show that $2K$ of any smooth compact complex two ball quotient is very ample, except possibly for four pairs of fake projective planes of minimal type, where $K$ is the canonical line bundle. For the four pairs of fake projective planes, sections of $2K_M$ give an embedding of $M$ except possibly for at most two points on $M$ .

Keywords

very ampleness bicanonical line bundle compact complex ball quotients fake projective planes canonical line bundle algebraic geometry

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@article{arxiv.1603.04978,
  title  = {Very ampleness of the bicanonical line bundle on compact complex two ball quotients},
  author = {Sai-Kee Yeung},
  journal= {arXiv preprint arXiv:1603.04978},
  year   = {2018}
}

Comments

In this revised version, an appendix giving some details for proof of the result for Cartwright-Steger surface is given

Very ampleness of the bicanonical line bundle on compact complex two ball quotients

Abstract

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