Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the second powers of Stanley-Reisner ideals   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.

21
The categories of this paper are: adap-org
15
The categories of this paper are: nucl-ex
8
The categories of this paper are: hep-ex
33
The categories of this paper are: plasm-ph
18
The categories of this paper are: econ
19
The categories of this paper are: eess
6
The categories of this paper are: astro-ph
22
The categories of this paper are: chao-dyn
29
The categories of this paper are: funct-an
30
The categories of this paper are: q-alg
37
The categories of this paper are: supr-con
24
The categories of this paper are: dg-ga
4
The categories of this paper are: cond-mat
20
The categories of this paper are: acc-phys
34
The categories of this paper are: chem-ph
32
The categories of this paper are: atom-ph