Fibers of rational maps and Rees algebras of their base ideals

Abstract

We consider a ratinonal map $\phi$ from m-dimensional projective space to n-dimensional projective space that is a parameterization of m-dimensional variety. Our main goal is to study the (m-1)-dimensional fibers of $\phi$ in relation with the m-th local cohomology modules of Rees algebra of its base ideal.

Keywords

• approximation complexes
• base ideals
• fibers of rational maps
• parameterizations
• rees algebras