Set-theoretically perfect ideals and residual intersections

Abstract

This paper studies algebraic residual intersections in rings with Serre's condition $S_s$. It demonstrates that a wide class of residual intersections is set theoretically perfect. This fact leads to determining a uniform upper bound for the multiplicity of residual intersections. In positive characteristic, it follows that residual intersections are cohomologically complete intersection, and hence, their variety is connected in codimension 1.