18 citations · 35 across the 18 of their papers we have counts for
21 papers
The Bourbaki Degree of Line Arrangements
Abbas Nasrollah Nejad, Samira Nouri
We study the Bourbaki degree of line arrangements in the projective plane and its interaction with the intersection lattice and the syzygies of the gradient ideal. We show that the…
Numerical invariants for three-generated ideals
Marcos Jardim, Felipe Monteiro, Abbas Nasrollah Nejad +1
We study numerical invariants of homogeneous ideals generated by three forms, with particular emphasis on the interaction between the initial degree of the syzygy module, the multi…
Jacobian algebras and variation of hyperplane sections
Giovanna Ilardi, Abbas Nasrollah Nejad, Saeed Tafazolian
We study the variation in moduli of hyperplane sections of a hypersurface with at most isolated singularities. Using the Milnor algebra , we give…
Closing two recent conjectures related to the Jacobian ideal of hyperplane arrangements
Abbas Nasrollah Nejad, Aron Simis
This work is about two conjectures stated by Burity--Simis--Tohăneanu regarding the Jacobian ideal of the defining polynomial of a central arrangement of hyperplanes. One settl…
The relation type of point configurations in the projective plane
Ethan Cotterill, Amir Mohammad Kach khaali, Abbas Nasrollah Nejad
We study the {\it relation type} of ideals of finite reduced sets of points in the projective plane; for a given ideal, this is the maximal -degree of a minimal generator of the…
The Bourbaki degree of the syzygy module of 2 4 matrices
Marcos Jardim, Felipe Monteiro, Abbas Nasrollah Nejad
We introduce and study the Bourbaki degree as a numerical invariant for \(2 \times 4\) matrices of homogeneous polynomials over a polynomial ring \(R = k[x_1, \dots, x_n]\). Th…
Veronese Avoiding Hypersurfaces
Giovanna Ilardi, Abbas Nasrollah Nejad, Saeed Tafazolian
We introduce Veronese-Avoiding hypersurfaces, inspired by the theory of associated forms of Alper--Isaev. In the smooth case, we reinterpret their criterion via Macaulay inverse sy…
Quasihomogeneous isolated singularities in terms of syzygies and foliations
Hamid Hassanzadeh, Abbas Nasrollah Nejad, Aron Simis
One considers quasihomogeneous isolated singularities of hypersurfaces in arbitrary dimensions through the lenses of three apparently quite apart themes: syzygies, singularity inva…
On Strong Lefschetz Property of 0-dimensional complete intersections and Veronese varieties
Alexandru Dimca, Giovanna Ilardi, Abbas Nasrollah Nejad
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 system…
The Bourbaki Degree of Plane Projective Curves
Marcos Jardim, Abbas Nasrollah Nejad, Aron Simis
Bourbaki sequences and Bourbaki ideals have been studied by several authors since its inception sixty years ago circa. Generic Bourbaki sequences have been thoroughly examined by t…
The Relation Type of Varieties
Maryam Akhavin, Abbas Nasrollah Nejad
In this paper, we introduce the notion of relation type of analytic and formal algebras and prove that it is well-defined and invariant by describing this notion in terms of the An…
Universal Decomposition Algebras Represent Endomorphisms
Ommolbanin Behzad, Abbas Nasrollah Nejad
The goal of this paper is to supply an explicit description of the universal decomposition algebra of the generic polynomial of degree into the product of two monic polynomials…
The Valabrega-Valla modules of monomial ideals
Abbas Nasrollah Nejad, Ali Akbar Yazdan Pour
In this paper, we focus on the initial degree and the vanishing of the Valabrega-Valla module of a pair of monomials ideals in a polynomials ring over a field $\math…
The module of Valabrega-Valla of the Jacobian ideal of points in projective plane
Abbas Nasrollah Nejad, Zahra Shahidi
The module of Valabrega-Valla of the Jacobian ideal of a reduced projective variety is the torsion of the Aluffi algebra. One considers the problem of its vanishing in the case…
Hypersurfaces with linear type singular loci
Amir Behzad Farrahy, Abbas Nasrollah Nejad
In this paper, necessary and sufficient criteria for the Jacobian ideal of a reduced hypersurface with isolated singularity to be of linear type, are presented. We prove that the g…
The Aluffi Algebra of a hypersurface with isolated singularity
Abbas Nasrollah Nejad
The Aluffi algebra is algebraic definition of characteristic cycles of a hypersurface in intersection theory. In this paper we focus on the Aluffi algebra of quasi-homogeneous and…
Tame graphs, clutters and their Rees algebras
Abbas Nasrollah Nejad, Ashkan Nikseresht, Ali Akbar Yazdan Pour +1
A tame ideal is an ideal such that the blowup of the affine space along is regular. In this paper, we give a combinatorial characterization of tame squaref…
The Aluffi algebra of the Jacobian of points in projective space: torsion-freeness
Abbas Nasrollah Nejad, Aron Simis, Rashid Zaare-Nahandi
The algebra in the title has been introduced by P. Aluffi. Let be ideals in the commutative ring . The (embedded) Aluffi algebra of on is an intermediate…
Monomial ideals with 3-linear resolutions
Marcel Morales, Abbas Nasrollah Nejad, Ali Akbar Yazdan Pour +1
In this paper, we study Cstelnuovo-Mumford regularity of square-free monomial ideals generated in degree 3. We define some operations on the clutters associated to such ideals and…
Aluffi torsion-free ideals
Abbas Nasrollah Nejad, Rashid Zaare-Nahandi
A special class of algebras which are intermediate between the symmetric and the Rees algebras of an ideal was introduced by P. Aluffi in 2004 to define characteristic cycle of a h…
The Aluffi Algebra
Abbas Nasrollah Nejad, Aron Simis
We deal with the quasi-symmetric algebra introduced by Paolo Aluffi, here named (embedded) Aluffi algebra. The algebra is a sort of "intermediate" algebra between the symmetric alg…