Monomial ideals and the failure of the Strong Lefschetz property
نویسندگان
چکیده
Abstract We give a sharp lower bound for the Hilbert function in degree d of artinian quotients $$\Bbbk [x_1,\ldots ,x_n]/I$$ k [ x 1 , … n ] / I failing Strong Lefschetz property, where I is monomial ideal generated $$d \ge 2$$ d ≥ 2 . also provide bounds other classes ideals, and connect our result to classification functions forcing property by Zanello Zylinski.
منابع مشابه
Monomial 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 کاملThe 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 کاملThe Strong Lefschetz Property and Simple Extensions
Stanley [4] showed that monomial complete intersections have the strong Lefschetz property. Extending this result we show that a simple extension of an Artinian Gorenstein algebra with the strong Lefschetz property has again the strong Lefschetz property. Introduction Let K be a field, A be a standard graded Artinian K-algebra and a ∈ A a homogeneous form of degree k. The element a is called a ...
متن کاملStrong Lefschetz Property under Reduction
Let n > 1 and G be the group SU(n) or Sp(n). This paper constructs compact symplectic manifolds whose symplectic quotient under a Hamiltonian G-action does not inherit the strong Lefschetz property .
متن کاملA Class of Hilbert Series and the Strong Lefschetz Property
We determine the class of Hilbert series H so that if M is a finitely generated zero-dimensional R-graded module with the strong Lefschetz property, then M ⊗k k[y]/(y ) has the strong Lefschetz property for y an indeterminate and all positive integers m if and only if the Hilbert series of M is in H. Given two finite graded R-modules M and N with the strong Lefschetz property, we determine suff...
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: Collectanea Mathematica
سال: 2021
ISSN: ['2038-4815', '0010-0757']
DOI: https://doi.org/10.1007/s13348-021-00324-7