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

Fibers of rational maps and Rees algebras of their base ideals