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arXiv · 1801.07672

Monomial ideals with tiny squares

Shalom Eliahou·Jürgen Herzog·Maryam Mohammadi Saem
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Abstract

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

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Shalom Eliahou, Jürgen Herzog, Maryam Mohammadi Saem. 2018-01-23. Monomial ideals with tiny squares. https://doi.org/10.1016/j.jalgebra.2018.07.037

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