In this paper, we study several properties of the second power (formula) of a Stanley-Reisner ideal I∆ of any dimension. As the main result, we prove that S/I∆ is Goren-stein whenever (formula) is Cohen-Macaulay over any field K. Moreover, we give a criterion for the second symbolic power of I∆ to satisfy (S2) and to coincide with the ordinary power, respectively. Finally, we provide new examples of Stanley-Reisner ideals whose second powers are Cohen-Macaulay.
ASJC Scopus subject areas
- Algebra and Number Theory