Fibers of rational maps and Rees algebras of their base ideals

Abstract

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

arXiv comment13 Pages