Abdallah Assi
YOU?
Author Swipe
View article: Geometry of Supermanifolds through Sheaf and Ringed Space Methods
Geometry of Supermanifolds through Sheaf and Ringed Space Methods Open
This paper introduces the concept of supermanifolds, viewed as the super-analogues of classical manifolds. Instead of treating supermanifolds as sets of points, we adopt an algebraic-geometric perspective, emphasizing the algebra of functi…
View article: New log-majorization results concerning eigenvalues and singular values and a complement of a norm inequality
New log-majorization results concerning eigenvalues and singular values and a complement of a norm inequality Open
The purpose of this paper is to establish new log-majorization results concerning eigenvalues and singular values which generalize some previous work related to a conjecture and an open question which were presented by R. Lemos and G. Soar…
View article: Semigroup associated with a free polynomial
Semigroup associated with a free polynomial Open
Let $\mathbb{K}$ be an algebraically closed field of characteristic zero and let $\mathbb{K}_{C}[[x_{1},...,x_{e}]]$ be the ring of formal power series in several variables with exponents in a line free cone $C$. We consider irreducible po…
View article: The plane Jacobian conjecture for rational curves
The plane Jacobian conjecture for rational curves Open
Let K be an algebraically closed field of characteristic zero and let f(x,y) be a nonzero polynomial of K[x,y]. We prove that if the generic element of the family $(f-λ)\_λ$ is a rational polynomial, and if the Jacobian J(f,g) is a nonzero…
View article: On canonical bases of a formal ${\mathbb K}-algebra
On canonical bases of a formal ${\mathbb K}-algebra Open
We study canonical bases of a subalgebra ${\bf A}={\mathbb K}[\![f_1,\dots,f_s]\!]\subseteq {\mathbb K}[\![x_1,\dots,x_n]\!]$ over a field ${\mathbb K}$, and we associate with ${\bf A}$ a fan called the canonical fan of $\bf A$. This gener…
View article: On canonical bases of a formal ${\\mathbb K}-algebra
On canonical bases of a formal ${\\mathbb K}-algebra Open
We study canonical bases of a subalgebra ${\\bf A}={\\mathbb\nK}[\\![f_1,\\dots,f_s]\\!]\\subseteq {\\mathbb K}[\\![x_1,\\dots,x_n]\\!]$ over a field\n${\\mathbb K}$, and we associate with ${\\bf A}$ a fan called the canonical fan\nof $\\b…
View article: Canonical bases of modules over one dimensional k-algebras
Canonical bases of modules over one dimensional k-algebras Open
Let K be a field and denote by K[t], the polynomial ring with coefficients in K. Set A = K[f1,. .. , fs], with f1,. .. , fs $\in$ K[t]. We give a procedure to calculate the monoid of degrees of the K algebra M = F1A + $\times$ $\times$ $\t…
View article: CONSTRUCTING THE SET OF COMPLETE INTERSECTION NUMERICAL SEMIGROUPS WITH A GIVEN FROBENIUS NUMBER
CONSTRUCTING THE SET OF COMPLETE INTERSECTION NUMERICAL SEMIGROUPS WITH A GIVEN FROBENIUS NUMBER Open
Delorme suggested that the set of all complete intersection numerical semigroups can be computed recursively. We have implemented this algorithm, and particularized it to several subfamilies of this class of numerical semigroups: free and …
View article: Frobenius vectors, Hilbert series and gluings of affine semigroups
Frobenius vectors, Hilbert series and gluings of affine semigroups Open
Let $S_1$ and $S_2$ be two affine semigroups, and let $S$ be the gluing\nof $S_1$ and $S_2$. Several invariants of $S$ are related to those of\n$S_1$ and $S_2$; we review some of the most important properties preserved under gluings.\nThe …
View article: FROBENIUS VECTORS, HILBERT SERIES AND GLUINGS
FROBENIUS VECTORS, HILBERT SERIES AND GLUINGS Open
Let S1 and S2 be two affine semigroups and let S be the gluing of S1 and S2. Several invariants of S are then related to those of S1 and S2; we review some of the most important properties preserved under gluings. The aim of this paper is …