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arXiv · 2504.07535

The v-numbers of Stanley-Reisner ideals from the viewpoint of Alexander dual complexes

Tatsuya Kataoka·Yuji Muta·Naoki Terai
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Abstract

We express the v-number of the Stanley-Reisner ideal in terms of its Alexander dual complex and prove that the v-number of a cover ideal is just two less than the initial degree of the its syzygy module. We give some relation between the v-number of the Stanley-Reisner ideal and the Serre-depth of the quotient ring of the second symbolic power of the Stanley-Reisner ideal of its Alexander dual. We also show that the v-number of the Stanley-Reisner ideal of a 2-pure simplicial complex is equal to the dimension of its Stanley-Reisner ring.

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Tatsuya Kataoka, Yuji Muta, Naoki Terai. 2025-04-10. The v-numbers of Stanley-Reisner ideals from the viewpoint of Alexander dual complexes. https://arxiv.org/abs/2504.07535

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