Thanks to Theorem 5.4, for $X$ a projective algebraic manifold of general type such that $R(X):=\oplus_{n\in\mathbb{N}}H^{0}(X,\mathcal{O}_{X}(nK_{X}))$ is finitely generated, $X$ has a unique birational model $V$ such that the above hypotheses hold. Thus we have a birational map $\pi:X\dashrightarrow V$ which is well defined outside an indeterminacy locus $S$ of codimension $\leq 2$. In particular $\pi^{*}(\omega+dd^{c}\varphi)$ is a closed positive current on $X-S$ that extends to a closed positive current $T$ on $X$ itself. The current $T$ defines a KE metric on $X-S$. It needs not be a singular KE metric on $X$ though, since its potentials may have logarithmic poles on $S$, in fact algebraic singularities of the form $\alpha\log(\sum|f_{i}|^{2})+O(1)$ $f_{i}$ holomorphic and $\alpha\in\mathbb{Q}_{>0}$. Moreover, $T$ lies in the canonical class of $X$ iff $X$ is a smooth minimal model as in [Ts].