Abstract
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. LetR be a regular local Nagata ring containing an infinite perfect fieldk, andI⊂R is an equidimensional radical ideal of heightr, such thatR/I is Cohen-Macaulay and a local complete intersection in codimension 1. Then for the ‘general’ linked idealJα, R/Jα is normal and Cohen-Macaulay.
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