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arXiv · 1111.6258

Alternative polarizations of Borel fixed ideals, Eliahou-Kervaire type resolution and discrete Morse theory

Ryota Okazaki·Kohji Yanagawa
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Abstract

We construct an Eliahou-Kervaire-like minimal free resolution of the alternative polarization $b-pol(I)$ of a Borel fixed ideal $I$. It yields new descriptions of the minimal free resolutions of $I$ itself and $I^sq$, where $(-)^sq$ is the squarefree operation in the shifting theory. These resolutions are cellular, and the (common) supporting cell complex is given by discrete Morse theory. If $I$ is generated in one degree, our description is equivalent to that of Nagel and Reiner.

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Ryota Okazaki, Kohji Yanagawa. 2011-11-27. Alternative polarizations of Borel fixed ideals, Eliahou-Kervaire type resolution and discrete Morse theory. https://arxiv.org/abs/1111.6258

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