scholarly journals The strong Lefschetz property of monomial complete intersections in two variables

2017 ◽  
Vol 69 (3) ◽  
pp. 359-375 ◽  
Author(s):  
Lisa Nicklasson
Keyword(s):  
Complete Intersections ◽  
Lefschetz Property ◽  
Strong Lefschetz Property

scholarly journals The strong Lefschetz property for complete intersections defined by products of linear forms

2019 ◽  
Vol 113 (1) ◽  
pp. 43-51
Author(s):  
Tadahito Harima ◽  
Akihito Wachi ◽  
Junzo Watanabe
Keyword(s):  
Complete Intersections ◽  
Linear Forms ◽  
Lefschetz Property ◽  
Strong Lefschetz Property ◽  
By Products

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

scholarly journals On the formality and strong Lefschetz property of symplectic manifolds – Erratum

2009 ◽  
Vol 147 (1) ◽  
pp. 255-255
Author(s):  
Taek Kyu Hwang ◽  
Jin Hong Kim
Keyword(s):  
Fundamental Group ◽  
Symplectic Manifold ◽  
Symplectic Manifolds ◽  
Finite Covering ◽  
Massey Product ◽  
Lefschetz Property ◽  
The Stability ◽  
Simply Connected ◽  
Open Question ◽  
Strong Lefschetz Property

Professor Vicente Muñoz kindly informed us that there is an inaccuracy in Lemma 3.5 of [1]. The correct statement of Lemma 3.5 is now that the fundamental group π1(X′) of the manifold X′ is Z, since the monodromy coming from φ8 does not imply that g4 = g4−1. Therefore, what we have actually constructed in Section 3 of [1] is a closed non-formal 8-dimensional symplectic manifold with π1 = Z whose triple Massey product is non-zero, so that the simply-connectedness in Theorem 1.1 should be dropped. As far as we know, the existence of a simply connected closed non-formal 8-dimensional symplectic manifold whose triple Massey product is non-zero still remains an open question. All other main results, especially Theorem 1.2 and Corollary 1.3, in [1] are not affected by this mistake. Furthermore, the stability of the non-formality under a finite covering as in Subsection 3.3 holds in general. We want to thank Professor Muñoz for his careful reading.

scholarly journals Canonical equivariant extensions using classical Hodge theory

2005 ◽  
Vol 2005 (8) ◽  
pp. 1277-1282 ◽  
Author(s):  
Christopher Allday
Keyword(s):  
Hodge Theory ◽  
Symplectic Manifolds ◽  
Lefschetz Property ◽  
Strong Lefschetz Property ◽  
Hamiltonian Actions

Lin and Sjamaar have used symplectic Hodge theory to obtain canonical equivariant extensions for Hamiltonian actions on closed symplectic manifolds that have the strong Lefschetz property. Here we obtain canonical equivariant extensions much more generally by means of classical Hodge theory.

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