Syzygy bundles and the weak Lefschetz property of monomial almost complete intersections

2021 ◽  
Vol 13 (2) ◽  
Author(s):  
David Cook II ◽  
Uwe Nagel
Keyword(s):  
Complete Intersections ◽  
Weak Lefschetz Property ◽  
Lefschetz Property

Complete intersections of quadrics and the Weak Lefschetz Property

2018 ◽  
Vol 70 (2) ◽  
pp. 283-294
Author(s):  
Alberto Alzati ◽  
Riccardo Re
Keyword(s):  
Complete Intersections ◽  
Weak Lefschetz Property ◽  
Lefschetz Property

scholarly journals On the weak Lefschetz property for vector bundles on P2

2021 ◽  
Vol 568 ◽  
pp. 22-34
Author(s):  
Gioia Failla ◽  
Zachary Flores ◽  
Chris Peterson
Keyword(s):  
Vector Bundles ◽  
Weak Lefschetz Property ◽  
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.

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