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 residual intersections admit free approaches i.e. perfect subideal with the same radical. 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 one.

28 pages, the previous title "A free Approach to Residual Intersections " changed to "Set-Theoretically Perfect Ideals and Residual Intersections", to appear in J. London Math. Soc