Zobrazeno 1 - 10
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pro vyhledávání: '"Abdallah, Nancy"'
The Jordan type $P_{A,\ell}$ of a linear form $\ell$ acting on a graded Artinian algebra $A$ over a field $\sf k$ is the partition describing the Jordan block decomposition of the multiplication map $m_\ell$, which is nilpotent. The Jordan degree typ
Externí odkaz:
http://arxiv.org/abs/2406.06322
Autor:
Abdallah, Nancy, McDaniel, Chris
We study a certain two-parameter family of non-standard graded complete intersections $A(m,n)$. In case $n=2$, we show that $A(m,2)$ has the strong Lefschetz property and the complex Hodge-Riemann property if and only if $m$ is even. This supports a
Externí odkaz:
http://arxiv.org/abs/2404.05098
Autor:
Abdallah, Nancy, Altafi, Nasrin, De Poi, Pietro, Fiorindo, Luca, Iarrobino, Anthony, Marques, Pedro Macias, Mezzetti, Emilia, Miró-Roig, Rosa M., Nicklasson, Lisa
We study Hilbert functions, Lefschetz properties, and Jordan type of Artinian Gorenstein algebras associated to Perazzo hypersurfaces in projective space. The main focus lies on Perazzo threefolds, for which we prove that the Hilbert functions are al
Externí odkaz:
http://arxiv.org/abs/2303.16768
Autor:
Abdallah, Nancy
We study the free resolutions of some Artin Gorenstein algebras of Hilbert function $(1,4,k,k,4,1)$ and we prove that all such algebras have the Strong Lefschetz property if they have the Weak Lefschetz property. In the case $k=4$ we prove that the H
Externí odkaz:
http://arxiv.org/abs/2302.14797
Let $R={\sf k}[x,y,z]$, the polynomial ring over a field $\sf k$. Several of the authors previously classified nets of ternary conics and their specializations over an algebraically closed field. We here show that when $\sf k$ is algebraically closed
Externí odkaz:
http://arxiv.org/abs/2302.00287
Autor:
Abdallah, Nancy, Schenck, Hal
A net in $\mathbb{P}^2$ is a configuration of lines $\mathcal A$ and points $X$ satisfying certain incidence properties. Nets appear in a variety of settings, ranging from quasigroups to combinatorial design to classification of Kac-Moody algebras to
Externí odkaz:
http://arxiv.org/abs/2208.01557
Autor:
Abdallah, Nancy, Schenck, Hal
In 1978, Stanley constructed an example of an Artinian Gorenstein (AG) ring $A$ with non-unimodal $H$-vector $(1,13,12,13,1)$. Migliore-Zanello later showed that for regularity $r=4$, Stanley's example has the smallest possible codimension $c$ for an
Externí odkaz:
http://arxiv.org/abs/2208.01536
Codimension two Artinian algebras $A$ have the strong and weak Lefschetz properties provided the characteristic is zero or greater than the socle degree. It is open to what extent such results might extend to codimension three AG algebras - the most
Externí odkaz:
http://arxiv.org/abs/2203.01258
We classify the orbits of nets of conics under the action of the projective linear group and we determine the specializations of these orbits, using geometric and algebraic methods. We study related geometric questions, as the parametrization of plan
Externí odkaz:
http://arxiv.org/abs/2110.04436
Autor:
Abdallah, Nancy, Schenck, Hal
Publikováno v:
In Journal of Symbolic Computation March-April 2024 121
