A Note on the $k$-Buchsbaum Property of Symbolic Powers of Stanley-Reisner Ideals

On a special class of Stanley-Reisner ideals

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 ...

Stanley-reisner Ideals Whose Powers Have Finite Length Cohomologies

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.

Buchsbaum Stanley–reisner Rings with Minimal Multiplicity

In this paper, we study non-Cohen–Macaulay Buchsbaum Stanley– Reisner rings with linear free resolution. In particular, for given integers c, d, q with c ≥ 1, 2 ≤ q ≤ d, we give an upper bound hc,d,q on the dimension of the unique non-vanishing homology H̃q−2(∆; k) of a d-dimensional Buchsbaum ring k[∆] with q-linear resolution and codimension c. Also, we discuss about existence for such Buchsba...

Symbolic Powers of Ideals in k[PN]

Locally Complete Intersection Stanley–reisner Ideals

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.