The Lefschetz Property for Componentwise Linear Ideals and Gotzmann Ideals
نویسندگان
چکیده
منابع مشابه
The Lefschetz Property for Componentwise Linear Ideals and Gotzmann Ideals
For standard graded Artinian K-algebras defined by componentwise linear ideals and Gotzmann ideals, we give conditions for the weak Lefschetz property in terms of numerical invariants of the defining ideals.
متن کاملSome Families of Componentwise Linear Monomial Ideals
Let R = k[x1, . . . , xn] be a polynomial ring over a field k. Let J = {j1, . . . , jt} be a subset of {1, . . . , n}, and let mJ ⊂ R denote the ideal (xj1 , . . . , xjt). Given subsets J1, . . . , Js of {1, . . . , n} and positive integers a1, . . . , as, we study ideals of the form I = m1 J1 ∩ · · · ∩ m as Js . These ideals arise naturally, for example, in the study of fat points, tetrahedral...
متن کاملMonomial Ideals, Almost Complete Intersections and the Weak Lefschetz Property
has maximal rank, i.e. it is injective or surjective. In this case, the linear form L is called a Lefschetz element of A. (We will often abuse notation and say that the corresponding ideal has the WLP.) The Lefschetz elements of A form a Zariski open, possibly empty, subset of (A)1. Part of the great interest in the WLP stems from the fact that its presence puts severe constraints on the possib...
متن کاملGotzmann Ideals of the Polynomial Ring
Let A = K[x1, . . . , xn] denote the polynomial ring in n variables over a field K. We will classify all the Gotzmann ideals of A with at most n generators. In addition, we will study Hilbert functions H for which all homogeneous ideals of A with the Hilbert function H have the same graded Betti numbers. These Hilbert functions will be called inflexible Hilbert functions. We introduce the notio...
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 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: 2004
ISSN: 0092-7872,1532-4125
DOI: 10.1081/agb-200036809