Corpus ID: 119316217

Poincare Series And Very Ampleness Criterion For Pluri-canonical Bundles

  title={Poincare Series And Very Ampleness Criterion For Pluri-canonical Bundles},
  author={Jujie Wu and Xu Wang},
  journal={arXiv: Complex Variables},
  • J. Wu, Xu Wang
  • Published 1 April 2015
  • Mathematics
  • arXiv: Complex Variables
Let $X$ be a compact quotient of a bounded domain in $\mathbb C^n$. Let $K_X$ be the canonical line bundle of $X$. In this paper, we shall introduce the notion of $S$ very ampleness for the pluri-canonical line bundles $mK_X$ by using the Poincar\'e series. The main result is an effective Seshadri constant criterion of $S$ very ampleness for $mK_X$. An elementary proof of surjectivity of the Poincar\'e map is also given. 
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