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The v-numbers of Stanley-Reisner ideals from the viewpoint of Alexander dual complexes
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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.
Forward citations
Cited by 2 Pith papers
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$\operatorname{v}$-numbers of integral closure filtrations of monomial ideals
For certain monomial ideals, the paper proposes explicit values and bounds for v-numbers of integral closure filtrations and shows they can be smaller than v-numbers of ordinary powers.
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