On a special class of Stanley-Reisner ideals
نویسنده
چکیده مقاله:
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 the generalized suspension of it in the Stanley-Reisner sense. Applications to Stanley-Reisner ideals and simplicial complexes are considered.
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 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 Rings and the Radicals of Lattice Ideals
In this article we associate to every lattice ideal IL,ρ ⊂ K[x1, . . . , xm] a cone σ and a graph Gσ with vertices the minimal generators of the Stanley-Reisner ideal of σ. To every polynomial F we assign a subgraph Gσ(F ) of the graph Gσ. Every expression of the radical of IL,ρ, as a radical of an ideal generated by some polynomials F1, . . . , Fs gives a spanning subgraph of Gσ, the ∪ s i=1Gσ...
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 کاملA Survey of Stanley-reisner Theory
We survey the Stanley-Reisner correspondence in combinatorial commutative algebra, describing fundamental applications involving Alexander duality, associated primes, f and h-vectors, and Betti numbers of monomial ideals.
متن کاملArithmetical ranks of Stanley-Reisner ideals of simplicial complexes with a cone
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...
متن کاملمنابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ذخیره در منابع من قبلا به منابع من ذحیره شده{@ msg_add @}
عنوان ژورنال
دوره 2 شماره 2
صفحات 25- 36
تاریخ انتشار 2014-12-01
با دنبال کردن یک ژورنال هنگامی که شماره جدید این ژورنال منتشر می شود به شما از طریق ایمیل اطلاع داده می شود.
میزبانی شده توسط پلتفرم ابری doprax.com
copyright © 2015-2023