On the second powers of Stanley-Reisner ideals

Details On the second powers of Stanley-Reisner ideals On the second powers of Stanley-Reisner ideals

2012-03-09

arxiv.org/abs/1203.1969v1

J. Commut. Algebra 3 (2011) 405-430

Mathematics

Commutative Algebra

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Scientific paper

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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