Minimal free resolutions for homogeneous ideals with Betti numbers 1, n, n,1
نویسندگان
چکیده
منابع مشابه
Betti Numbers and Shifts in Minimal Graded Free Resolutions
Let S = K[x1, . . . ,xn] be a polynomial ring and R = S/I where I ⊂ S is a graded ideal. The Multiplicity Conjecture of Herzog, Huneke, and Srinivasan states that the multiplicity of R is bounded above by a function of the maximal shifts in the minimal graded free resolution of R over S as well as bounded below by a function of the minimal shifts if R is Cohen–Macaulay. In this paper we study t...
متن کاملMinimal Graded Betti Numbers and Stable Ideals
Let k be a field, and let R = k[x1, x2, x3]. Given a Hilbert function H for a cyclic module over R, we give an algorithm to produce a stable ideal I such that R/I has Hilbert function H and uniquely minimal graded Betti numbers among all R/J with the same Hilbert function, where J is another stable ideal in R. We also show that such an algorithm is impossible in more variables and disprove a re...
متن کاملFREE MINIMAL RESOLUTIONS AND THE BETTI NUMBERS OF THE SUSPENSION OF AN n-GON
Consider the general n-gon with vertices at the points 1,2, . . . ,n. Then its suspension involves two more vertices, say at n+1 and n+2. Let R be the polynomial ring k[x1,x2, . . . ,xn], where k is any field. Then we can associate an ideal I to our suspension in the Stanley-Reisner sense. In this paper, we find a free minimal resolution and the Betti numbers of the R-module R/I.
متن کاملComponentwise Linear Ideals with Minimal or Maximal Betti Numbers
We characterize componentwise linear monomial ideals with minimal Taylor resolution and consider the lower bound for the Betti numbers of componentwise linear ideals. INTRODUCTION Let S = K[x1, . . . ,xn] denote the polynomial ring in n variables over a field K with each degxi = 1. Let I be a monomial ideal of S and G(I) = {u1, . . . ,us} its unique minimal system of monomial generators. The Ta...
متن کاملBetti numbers and minimal free resolutions for multi-state system reliability bounds
The paper continues work on monomial ideals in system reliability began by Giglio and Wynn [GW04] following work in discrete tube theory by Naiman and Wynn [NW92, NW97]. The key component is that of multigraded Betti numbers, and an algorithm using MayerVietoris trees by the first author [dC06] is the main tool. First a mapping must be made between the states of a multistate system and a monomi...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Communications in Algebra
سال: 2019
ISSN: 0092-7872,1532-4125
DOI: 10.1080/00927872.2018.1552281