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arXiv · 1807.05028

Polarization and spreading of monomial ideals

Mircea Cimpoeas
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Abstract

We characterize the monomial ideals $I\subset K[x_1,\ldots,x_n]$ with the property that the polarization $I^p$ and $I^{\sigma^n}:=$ the ideal obtained from $I$ by the $n$-th iterated squarefree operator $\sigma$ are isomorphic via a permutation of variables. We give several methods to construct such ideals. We also compare the depth and sdepth of $I$ and $I^{\sigma^n}$.

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Mircea Cimpoeas. 2018-07-13. Polarization and spreading of monomial ideals. https://doi.org/10.1080/00927872.2019.1632324

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