Cohen-Macaulay and (S₂) Properties of the Second Power of Squarefree Monomial Ideals

Abstract

We show that Cohen-Macaulay and (S 2 ) properties are equivalent for the second power of an edge ideal. We give an example of a Gorenstein squarefree monomial ideal I such that S / I 2 satisfies the Serre condition (S 2 ), but is not Cohen-Macaulay.

Keywords

• Stanley-Reisner ideal
• edge ideal
• Cohen-Macaulay
• (S2) condition