Let $f:X\rightarrow Y$ be a surjective birational morphism of varieties. Suppose the center of the birational morphism is $Z$ and $f:f^{-1}(Z)\rightarrow Z$ is a $\mathbb{P}^n$-bundle. Consider the relative tangent sheaf $T_f$. It is obviously torsion sheaf supported on $f^{-1}(Z)$. This torsion sheaf $det$ $T_f|_{f^{-1}(Z)}$ is a line bundle on $f^{-1}(Z)$. Can this line bundle be extended to whole of X as a line bundle?

What i am asking is how to define a relative ample line bundle in some canonical way for a birational morphism of above type? For a projective bundle for example the line bundle i am asking is : relative tangent bundle.