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arXiv · 2609.37112

The $\mathrm{v}$-number of powers of ideals associated with chessboard complexes

Wenjie Huo·Guangjun Zhu·Jiaxin Li
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Abstract

We study the $\mathrm{v}$-numbers of ordinary and symbolic powers of the facet ideal and the Stanley--Reisner ideal of a chessboard complex. Exact formulas are established for the $\mathrm{v}$-numbers of ordinary and symbolic powers of the Stanley--Reisner ideal, as well as symbolic powers of the facet ideal. Furthermore, we show that the $\mathrm{v}$-number function of the ordinary powers is asymptotically linear.

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Wenjie Huo, Guangjun Zhu, Jiaxin Li. 2026-09-29. The $\mathrm{v}$-number of powers of ideals associated with chessboard complexes. https://arxiv.org/abs/2609.37112

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