The weak Lefschetz property, monomial ideals, and lozenges
نویسندگان
چکیده
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 کاملIdeals of General Forms and the Ubiquity of the Weak Lefschetz Property
Let d1, . . . , dr be positive integers and let I = (F1, . . . , Fr) be an ideal generated by forms of degrees d1, . . . , dr, respectively, in a polynomial ring R with n variables. With no further information virtually nothing can be said about I, even if we add the assumption that R/I is Artinian. Our first object of study is the case where the Fi are chosen generally, subject only to the deg...
متن کاملThe Strength of the Weak Lefschetz Property
We study a number of conditions on the Hilbert function of a level artinian algebra which imply the Weak Lefschetz Property (WLP). Possibly the most important open case is whether a codimension 3 SI-sequence forces the WLP for level algebras. In other words, does every codimension 3 Gorenstein algebra have the WLP? We give some new partial answers to this old question: we prove an affirmative a...
متن کاملGeneric Initial Ideals and Graded Artinian Level Algebras Not Having the Weak-lefschetz Property
We find a sufficient condition that H is not level based on a reduction number. In particular, we prove that a graded Artinian algebra of codimension 3 with Hilbert function H = (h0, h1, . . . , hd−1 > hd = hd+1) cannot be level if hd ≤ 2d + 3, and that there exists a level Osequence of codimension 3 of type H for hd ≥ 2d+k for k ≥ 4. Furthermore, we show that H is not level if β1,d+2(I ) = β2,...
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ژورنال
عنوان ژورنال: Illinois Journal of Mathematics
سال: 2011
ISSN: 0019-2082
DOI: 10.1215/ijm/1355927041