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Bertini theorems for ideals linked to a given ideal

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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 idealJ α, R/Jα is normal and Cohen-Macaulay.

The proofs involve a combination of the method of basic elements, applied to suitable blow ups.

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  1. School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, 400 005, Bombay, India

    Trivedi Vijaylaxmi

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  1. Trivedi Vijaylaxmi
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Vijaylaxmi, T. Bertini theorems for ideals linked to a given ideal. Proc. Indian Acad. Sci. (Math. Sci.) 104, 305–331 (1994). https://doi.org/10.1007/BF02863411

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  • DOI: https://doi.org/10.1007/BF02863411

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