Related papers: On Strong Lefschetz Property of 0-dimensional comp…
We show that the Strong Lefschetz Property in degree 1 for a homogeneous 0-dimensional complete intersection holds if the corresponding associated form, the Macaulay inverse systems, has a non-zero discriminant.
Motivated by the foundational result that a monomial complete intersection has the strong Lefschetz property (SLP) in characteristic zero, it is natural to ask when monomial almost complete intersections have the SLP. In this paper, using…
We prove that any quadratic complete intersection with certain action of the symmetric group has the strong Lefschetz property over a field of characteristic zero. As a consequence of it we construct a new class of homogeneous complete…
We consider the conjecture that all artinian height 4 complete intersections of forms of the same degree $d$ have the Weak Lefschetz Property (WLP). We translate this problem to one of studying the general hyperplane section of a certain…
In this paper, we prove that any Artinian complete intersection homogeneous ideal $I$ in $K[x_0,\cdots,x_n]$ generated by $n+1$ forms of degree $d\ge 2$ satisfies the weak Lefschetz property (WLP) in degree $t< d+\lceil \frac{d}{n} \rceil$.…
We prove, in any positive characteristic, Parseval-Rayleigh identities for the residue map of a homogeneous complete intersection. As an application, we give a conceptual proof of the folklore fact that generic homogeneous complete…
Stanley proved that, in characteristic zero, all artinian monomial complete intersections have the strong Lefschetz property. We provide a positive characteristic complement to Stanley's result in the case of artinian monomial complete…
In this paper we classify the monomial complete intersection algebras, in two variables, and of positive characteristic, which has the strong Lef- schetz property. Together with known results, this gives a complete classi- fication of the…
We prove the strong Lefschetz property for certain complete intersections defined by products of linear forms, using a characterization of the strong Lefschetz property in terms of central simple modules.
A graded Artinian algebra $A$ has the Weak Lefschetz Property if there exists a linear form $\ell$ such that the multiplication map by $\ell:[A]_i\to [A]_{i+1}$ has maximum rank in every degree. The linear forms satisfying this property…
It is well known that a monomial complete intersection has the strong Lefschetz property in characteristic zero. This property is equivalent to the statement that any power of the sum of the variables is a maximal rank element on the…
The Hard Lefschetz Property (HLP) has recently been formulated in the context of isometric flows without singularities on manifolds. In this category, two versions of the HLP (transverse and not) have been proven to be equivalent, thus…
We study the positivity of complete intersections of nef classes. We first give a sufficient and necessary characterization on the complete intersection classes which have hard Lefschetz property on a compact complex torus, equivalently, in…
Let $A=\pmb k[x_1,...,x_n]/{(x_1^d,...,x_n^d)}$, where $\pmb k$ is an infinite field. If $\pmb k$ has characteristic zero, then Stanley proved that $A$ has the Weak Lefschetz Property (WLP). Henceforth, $\pmb k$ has positive characteristic…
In this paper we study the Lefschetz properties of monomial complete intersections in positive characteristic. We give a complete classification of the strong Lefschetz property when the number of variables is at least three, which proves a…
For zero-dimensional complete intersections with homogeneous ideal generators of equal degrees over an algebraically closed field of characteristic zero, we give a combinatorial proof of the smoothness of the corresponding catalecticant…
We generalize some properties related to Hilbert series and Lefschetz properties of Milnor algebras of projective hypersurfaces with isolated singularities to the more general case of an almost complete intersection ideal $J$ of dimension…
Every artinian quotient of $K[x,y]$ has the strong Lefschetz property if $K$ is a field of characteristic zero or is an infinite field whose characteristic is greater than the regularity of the quotient. We improve this bound in the case of…
A standard graded artinian monomial complete intersection algebra $A=\Bbbk[x_1,x_2,\ldots,x_n]/(x_1^{a_1},x_2^{a_2},\ldots,x_n^{a_n})$, with $\Bbbk$ a field of characteristic zero, has the strong Lefschetz property due to Stanley in 1980.…
The Hard Lefschetz Property (HLP) is an important property which has been studied in several categories of the symplectic world. For Sasakian manifolds, this duality is satisfied by the basic cohomology (so, it is a transverse property),…