Bertini theorems for ideals linked to a given ideal

Trivedi Vijaylaxmi

doi:10.1007/BF02863411

Bertini theorems for ideals linked to a given ideal

Trivedi Vijaylaxmi

Mathematics

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3 Scopus citations

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. Let R be a regular local Nagata ring containing an infinite perfect field k, and I⊂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_α, R/J_α is normal and Cohen-Macaulay. The proofs involve a combination of the method of basic elements, applied to suitable blow ups.

Original language	English
Pages (from-to)	305-331
Number of pages	27
Journal	Proceedings of the Indian Academy of Sciences: Mathematical Sciences
Volume	104
Issue number	2
DOIs	https://doi.org/10.1007/BF02863411
State	Published - May 1994

Keywords

Linkage
local Bertini theorem
Nash blow up
r-fold basic elements

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10.1007/BF02863411

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N2 - 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⊂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 α, R/Jα is normal and Cohen-Macaulay. The proofs involve a combination of the method of basic elements, applied to suitable blow ups.

AB - 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⊂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 α, R/Jα is normal and Cohen-Macaulay. The proofs involve a combination of the method of basic elements, applied to suitable blow ups.

KW - Linkage

KW - local Bertini theorem

KW - Nash blow up

KW - r-fold basic elements

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EP - 331

JO - Proceedings of the Indian Academy of Sciences: Mathematical Sciences

JF - Proceedings of the Indian Academy of Sciences: Mathematical Sciences

IS - 2

ER -

Bertini theorems for ideals linked to a given ideal

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Keywords

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