Monomial ideals with tiny squares

Let \(I \subset K[x,y]\) be a monomial ideal. How small can \(\mu(I^2)\) be in terms of \(\mu(I)\)? It has been expected that the inequality \(\mu(I^2) > \mu(I)\) should hold whenever \(\mu(I) \ge 2\). Here we disprove this expectation and provide a somewhat surprising answer to the above questio...

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Bibliographic Details
Published in:arXiv.org 2018-01
Main Authors: Eliahou, Shalom, Herzog, Jürgen, Maryam Mohammadi Saem
Format: Article
Language:English
Online Access:Get full text
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Summary:Let \(I \subset K[x,y]\) be a monomial ideal. How small can \(\mu(I^2)\) be in terms of \(\mu(I)\)? It has been expected that the inequality \(\mu(I^2) > \mu(I)\) should hold whenever \(\mu(I) \ge 2\). Here we disprove this expectation and provide a somewhat surprising answer to the above question.
ISSN:2331-8422
DOI:10.48550/arxiv.1801.07672