for an $n$-gon with vertices at points $1,2,cdots,n$, the betti numbers of its suspension, the simplicial complex that involves two more vertices $n+1$ and $n+2$, is known. in this paper, with a constructive and simple proof, wegeneralize this result to find the minimal free resolution and betti numbers of the $s$-module $s/i$ where  $s=k[x_{1},cdots, x_{n}]$ and $i$ is the associated ideal to ...

In this paper, we prove that the Stanley–Reisner ideal of any connected simplicial complex of dimension ≥ 2 that is locally complete intersection is a complete intersection ideal. As an application, we show that the Stanley–Reisner ideal whose powers are Buchsbaum is a complete intersection ideal.

Given a simplicial complex, it is easy to construct a generic deformation of its Stanley-Reisner ideal. The main question under investigation in this paper is how to characterize the simplicial complexes such that their Stanley-Reisner ideals have Cohen-Macaulay generic deformations. Algorithms are presented to construct such deformations for matroid complexes, shifted complexes, and tree compl...

When a cone is added to a simplicial complex ∆ over one of its faces, we investigate the relation between the arithmetical ranks of the StanleyReisner ideals of the original simplicial complex and the new simplicial complex ∆′. In particular, we show that the arithmetical rank of the Stanley-Reisner ideal of ∆′ equals the projective dimension of the Stanley-Reisner ring of ∆′ if the correspondi...

Let I ⊂ K[x1, . . . , xn] be a zero-dimensional monomial ideal, and ∆(I) be the simplicial complex whose Stanley–Reisner ideal is the polarization of I. It follows from a result of Soleyman Jahan that ∆(I) is shellable. We give a new short proof of this fact by providing an explicit shelling. Moreover, we show that ∆(I) is even vertex decomposable. The ideal L(I), which is defined to be the Sta...

For an $n$-gon with vertices at points $1,2,cdots,n$, the Betti numbers of its suspension, the simplicial complex that involves two more vertices $n+1$ and $n+2$, is known. In this paper, with a constructive and simple proof, wegeneralize this result to find the minimal free resolution and Betti numbers of the $S$-module $S/I$ where  $S=K[x_{1},cdots, x_{n}]$ and $I$ is the associated ideal to ...

Recently, Nevo introduced the notion of strongly edge decomposable spheres. In this paper, we characterize the algebraic shifted complex of those spheres. Algebraically, this result yields the characterization of the generic initial ideal of the Stanley–Reisner ideal of Gorenstein* complexes having the strong Lefschetz property in characteristic 0.

We show that the Stanley-Reisner ideal of the one-dimensional simplicial complex whose diagram is an n-gon is always a set-theoretic complete intersection in any positive characteristic.

We introduce a class of Stanley-Reisner ideals called generalized complete intersection, which is characterized by the property that all the residue class rings of powers of the ideal have FLC. We also give a combinatorial characterization of such ideals.