  We consider a rational map $\phi: \mathbb{P}_k^{m} \dashrightarrow
\mathbb{P}_k^n$ that is a parameterization of an $m$-dimensional variety. Our
main goal is to study the $(m-1)$-dimensional fibers of $\phi$ in relation to
the $m$-th local cohomology modules of the Rees algebra of its base ideal.
