skip to main content
US FlagAn official website of the United States government
dot gov icon
Official websites use .gov
A .gov website belongs to an official government organization in the United States.
https lock icon
Secure .gov websites use HTTPS
A lock ( lock ) or https:// means you've safely connected to the .gov website. Share sensitive information only on official, secure websites.


Search for: All records

Creators/Authors contains: "Faridi, Sara"

Note: When clicking on a Digital Object Identifier (DOI) number, you will be taken to an external site maintained by the publisher. Some full text articles may not yet be available without a charge during the embargo (administrative interval).
What is a DOI Number?

Some links on this page may take you to non-federal websites. Their policies may differ from this site.

  1. Abstract A major open question in the theory of Gorenstein liaison is whether or not every arithmetically Cohen–Macaulay subscheme of can be G‐linked to a complete intersection. Migliore and Nagel showed that if such a scheme is generically Gorenstein (e.g., reduced), then, after re‐embedding so that it is viewed as a subscheme of , indeed it can be G‐linked to a complete intersection. Motivated by this result, we consider techniques for constructing G‐links on a scheme from G‐links on a closely related reduced scheme. Polarization is a tool for producing a squarefree monomial ideal from an arbitrary monomial ideal. Basic double G‐links on squarefree monomial ideals can be induced from vertex decompositions of their Stanley–Reisner complexes. Given a monomial ideal and a vertex decomposition of the Stanley–Reisner complex of its polarization , we give conditions that allow for the lifting of an associated basic double G‐link of to a basic double G‐link of itself. We use the relationship we develop in the process to show that the Stanley–Reisner complexes of polarizations of stable Cohen– Macaulay monomial ideals are vertex decomposable. We then introduce and study polarization of a Gröbner basis of an arbitrary homogeneous ideal and give a relationship between geometric vertex decomposition of a polarization and elementary G‐biliaison that is analogous to our result on vertex decomposition and basic double G‐linkage. 
    more » « less
    Free, publicly-accessible full text available December 12, 2026