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

2025/04/10 by Kataoka, Tatsuya, Naoki Terai, Muta, Yuji +1 · 3 citations
Mathematics · Computer Science · #Commutative Algebra and Its Applications #Advanced Combinatorial Mathematics #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.2504.07535

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.

Cited by

• The Serre depth of Stanley-Reisner rings and the depth of their symbolic powers
• v-numbers of integral closure filtrations of monomial ideals
• Comparing the v-number and h-polynomials of edge ideals

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