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

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 $M$.

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