On the second powers of Stanley-Reisner ideals

Abstract

In this paper, we study several properties of the second power $I_{\Delta }^2$ of a Stanley-Reisner ideal $I_{\Delta }$ of any dimension. As the main result, we prove that $S/I_{\Delta }$ is Gorenstein whenever $S/I_{\Delta }^2$ is Cohen-Macaulay over any field $K$. Moreover, we give a criterion for the second symbolic power of $I_{\Delta }$ to satisfy $(S_2)$ and to coincide with the ordinary power, respectively. Finally, we provide new examples of Stanley-Reisner ideals whose second powers are Cohen-Macaulay.

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References in corpus (4)

• Combinatorial characterizations of generalized Cohen-Macaulay monomial ideals
• Equality of ordinary and symbolic powers of Stanley-Reisner ideals
• Cohen-Macaulayness of large powers of Stanley-Reisner ideals
• Cohen--Macaulaynees for symbolic power ideals of edge ideals