Pluricanonical systems of projective varieties of general type II

This is a revised version of the second half of my paper math.AG/9909021. We prove that there exists a positive integer $\nu_{n}$ depending only on $n$ such that for every smooth projective $n$-fold of general type $X$ defined over complex numbers, $\mid mK_{X}\mid$ gives a birational rational map from $X$ into a projective space for every $m\geq \nu_{n}$.