BERTINI THEOREMS FOR IDEALS LINKED TO A GIVEN IDEAL

We prove a generalization of Flenner's local Bertini theorem for complete intersections. More generally, we study properties of the 'general' ideal linked to a given ideal. Our results imply the following. Let R be a regular local Nagata ring containing an infinite perfect field k, and I subset-of R is an equidimensional radical ideal of height r, such that R/I is Cohen-Macaulay and a local complete intersection in codimension 1. Then for the 'general' linked ideal J(alpha), R/J(alpha) is normal and Cohen-Macaulay. The proofs involve a combination of the method of basic elements, applied to suitable blow ups.