Cohen-Macaulayness of large powers of Stanley-Reisner ideals

By Naoki Terai, Ngô Viêt Trung. 2010

70 citations recorded by the source corpus.

We prove that for m > 2, the m-th symbolic power of a Stanley-Reisner ideal is Cohen-Macaulay if and only if the simplicial complex is a matroid. Similarly, the m-th ordinary power is Cohen-Macaulay for some m > 2 if and only if the complex is a complete intersection. These results solve several open questions on the Cohen-Macaulayness of ordinary and symbolic powers of Stanley-Reisner ideals. Moreover, they have interesting consequences on the Cohen-Macaulayness of symbolic powers of facet ideals and cover ideals.

Subfields: Algebra and Number Theory, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/4ab050eddde2fd3004c24740059f887c5ae7887b

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In Algebra and Number Theory

In Geometry and Topology

Citations in the corpus

Matroid configurations and symbolic powers of their ideals (2015, background): “e intersection, and so ϕ∗(Pi)m is Cohen-Macaulay, we get ϕ∗(I∆)mRP = ϕ∗(Pi)mRP. This implies ϕ∗(I∆)(m) = Tt i=1 ϕ∗(Pi) m, as desired. Assume now that s ≤ c + 1. It was shown independently in [31] and [29] that, for each positive integer m, the ideal I(m) ∆ = \t j=1 Pm j is Cohen-Macaulay. Hence Lemm”
Depth and regularity of powers of sums of ideals (2015, background): “For instance, see [14, 15, 17, 20, 22, 23, 26] for studies on depth of powers of ideals, and see [1, 3, 6, 7, 8, 11, 10, 13, 19, 21, 24] for studies on regularity of powers of ideals.”