scholarly journals Hilbert functions of Artinian Gorenstein algebras with the strong Lefschetz property

2021 ◽  
pp. 1
Author(s):  
Nasrin Altafi
Keyword(s):  
Hilbert Functions ◽  
Gorenstein Algebras ◽  
Lefschetz Property ◽  
Strong Lefschetz Property ◽  
Artinian Gorenstein Algebras

scholarly journals Hilbert functions of Sn-stable artinian Gorenstein algebras

2016 ◽  
Vol 458 ◽  
pp. 53-70 ◽  
Author(s):  
Anthony V. Geramita ◽  
Andrew H. Hoefel ◽  
David L. Wehlau
Keyword(s):  
Hilbert Functions ◽  
Gorenstein Algebras ◽  
Artinian Gorenstein Algebras

scholarly journals On the Weak Lefschetz Property for artinian Gorenstein algebras of codimension three

2014 ◽  
Vol 403 ◽  
pp. 48-68 ◽  
Author(s):  
Mats Boij ◽  
Juan Migliore ◽  
Rosa M. Miró-Roig ◽  
Uwe Nagel ◽  
Fabrizio Zanello
Keyword(s):  
Gorenstein Algebras ◽  
Weak Lefschetz Property ◽  
Lefschetz Property ◽  
Artinian Gorenstein Algebras

scholarly journals Monomial ideals and the failure of the Strong Lefschetz property

2021 ◽  
Author(s):  
Nasrin Altafi ◽  
Samuel Lundqvist
Keyword(s):  
Lower Bound ◽  
Lower Bounds ◽  
Hilbert Function ◽  
Monomial Ideal ◽  
Monomial Ideals ◽  
Hilbert Functions ◽  
Lefschetz Property ◽  
Strong Lefschetz Property ◽  
Sharp Lower Bound

AbstractWe 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 , … , x n ] / I failing the Strong Lefschetz property, where I is a monomial ideal generated in degree $$d \ge 2$$ d ≥ 2 . We also provide sharp lower bounds for other classes of ideals, and connect our result to the classification of the Hilbert functions forcing the Strong Lefschetz property by Zanello and Zylinski.

The Strong Lefschetz Property and the Schur–Weyl Duality

2013 ◽  
pp. 211-234
Author(s):  
Tadahito Harima ◽  
Toshiaki Maeno ◽  
Hideaki Morita ◽  
Yasuhide Numata ◽  
Akihito Wachi ◽  
...  
Keyword(s):  
Weyl Duality ◽  
Lefschetz Property ◽  
Strong Lefschetz Property

Cohomology Rings and the Strong Lefschetz Property

2013 ◽  
pp. 189-199
Author(s):  
Tadahito Harima ◽  
Toshiaki Maeno ◽  
Hideaki Morita ◽  
Yasuhide Numata ◽  
Akihito Wachi ◽  
...  
Keyword(s):  
Cohomology Rings ◽  
Lefschetz Property ◽  
Strong Lefschetz Property

scholarly journals The Geometry of the Weak Lefschetz Property and Level Sets of Points

2008 ◽  
Vol 60 (2) ◽  
pp. 391-411 ◽  
Author(s):  
Juan C. Migliore
Keyword(s):  
Level Set ◽  
Level Sets ◽  
Hilbert Function ◽  
Worst Case ◽  
Weak Lefschetz Property ◽  
Lefschetz Property ◽  
Strong Lefschetz Property ◽  
Set Of Points

AbstractIn a recent paper, F. Zanello showed that level Artinian algebras in 3 variables can fail to have the Weak Lefschetz Property (WLP), and can even fail to have unimodal Hilbert function. We show that the same is true for the Artinian reduction of reduced, level sets of points in projective 3-space. Our main goal is to begin an understanding of how the geometry of a set of points can prevent its Artinian reduction from having WLP, which in itself is a very algebraic notion. More precisely, we produce level sets of points whose Artinian reductions have socle types 3 and 4 and arbitrary socle degree ≥ 12 (in the worst case), but fail to have WLP. We also produce a level set of points whose Artinian reduction fails to have unimodal Hilbert function; our example is based on Zanello's example. Finally, we show that a level set of points can have Artinian reduction that has WLP but fails to have the Strong Lefschetz Property. While our constructions are all based on basic double G-linkage, the implementations use very different methods.

scholarly journals The strong Lefschetz property of the coinvariant ring of the Coxeter group of type H4

2007 ◽  
Vol 318 (2) ◽  
pp. 1032-1038 ◽  
Author(s):  
Yasuhide Numata ◽  
Akihito Wachi
Keyword(s):  
Coxeter Group ◽  
Lefschetz Property ◽  
Strong Lefschetz Property
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