18 citations · 35 across the 18 of their papers we have counts for
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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…