7 papers
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--TohÄneanu regarding the Jacobian ideal of the defining polynomial of a central arrangement of hyperplanes. One sett…
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 \(R = k[x_1, \dots, x_n]\). T…
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…