# Poincare Series And Very Ampleness Criterion For Pluri-canonical Bundles

@article{Wu2015PoincareSA, title={Poincare Series And Very Ampleness Criterion For Pluri-canonical Bundles}, author={Jujie Wu and Xu Wang}, journal={arXiv: Complex Variables}, year={2015} }

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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