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arXiv · 2112.11726

Some homological properties of Borel type ideals

Jürgen Herzog·Somayeh Moradi·Masoomeh Rahimbeigi·Guangjun Zhu
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Abstract

We study ideals of Borel type, including $k$-Borel ideals and $t$-spread Veronese ideals. We determine their free resolutions and their homological shift ideals. The multiplicity and the analytic spread of equigenerated squarefree principal Borel ideals are computed. For the multiplicity, the result is given under an additional assumption which is always satisfied for squarefree principal Borel ideals. These results are used to analyze the behaviour of height, multiplicity and analytic spread of the homological shift ideals $HS_j(I)$ as functions of $j$, when $I$ is an equigenerated squarefree Borel ideal.

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Jürgen Herzog, Somayeh Moradi, Masoomeh Rahimbeigi, Guangjun Zhu. 2021-12-22. Some homological properties of Borel type ideals. https://arxiv.org/abs/2112.11726

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