The Stanley-Reisner ideals of polygons as set-theoretic complete intersections
نویسندگان
چکیده
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.
منابع مشابه
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 ...
متن کاملGeneralized Complete Intersections with Linear Resolutions
We determine the simplicial complexes ∆ whose Stanley-Reisner ideals I∆ have the following property: for all n ≥ 1 the powers In ∆ have linear resolutions and finite length local cohomologies.
متن کاملVertex Decomposable Simplicial Complexes Associated to Path Graphs
Introduction Vertex decomposability of a simplicial complex is a combinatorial topological concept which is related to the algebraic properties of the Stanley-Reisner ring of the simplicial complex. This notion was first defined by Provan and Billera in 1980 for k-decomposable pure complexes which is known as vertex decomposable when . Later Bjorner and Wachs extended this concept to non-pure ...
متن کاملLocally 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.
متن کاملStanley-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.
متن کامل