TL;DR
This paper investigates how the Cohen-Macaulay property is preserved under linkage in local rings and explores the relationship between linked modules' properties and local cohomology.
Contribution
It demonstrates conditions under which Cohen-Macaulayness is preserved under linkage and analyzes the connection between (S_n) loci and local cohomology attached primes.
Findings
Cohen-Macaulayness is preserved under linkage under mild conditions.
The (S_n) locus of linked modules relates to attached primes of local cohomology.
Provides new insights into the structure of linked modules in Cohen-Macaulay rings.
Abstract
Let R be a Cohen-Macaulay local ring. It is shown that under some mild conditions, the Cohen-Macaulayness property is preserved under linkage. We also study the connection of (S_n) locus of a horizontally linked module and the attached primes of certain local cohomology modules of its linked module.
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