Boulos El Hilany

activity

20152019

collaborators

5 papers

math.AG2019

A note on polynomial maps having fibers of maximal dimension

Boulos El Hilany

For any two integers $k, n$ , $2 \leq k \leq n$ , let $f : (C^{*})^{n} \to C^{k}$ be a generic polynomial map with given Newton polytopes. It is known that points, whose…

math.AG2019

Describing the Jelonek set of polynomial maps via Newton polytopes

Boulos El Hilany

Let $\K=\C$, or $R$ , and $S_{f}$ be the set of points in $\K^n$ at which a polynomial map $f:\K^n\rightarrow\K^n$ is non-proper. Jelonek proved that $S_{f}$ is a semi-algebraic set th…

math.AG2019

Counting isolated points outside the image of a polynomial map

Boulos El Hilany

We consider a generic family of polynomial maps $f := (f_{1}, f_{2}) : C^{2} \to C^{2}$ with given supports of polynomials, and degree $d (f) := max (d e g f_{1}, d e g f_{2})$ .…

math.AG2016

Characterization of circuits supporting polynomial systems with the maximal number of positive solutions

Boulos El Hilany

A polynomial system with $n$ equations in $n$ variables supported on a set $W \subset R^{n}$ of $n + 2$ points has at most $n + 1$ non-degenerate positive solutions. Mor…

math.AG2015

A sharp bound on the number of real intersection points of a sparse plane curve with a line

Frédéric Bihan, Boulos El Hilany

We prove that the number of real intersection points of a real line with a real plane curve defined by a polynomial with at most t monomials is either infinite or does not exceed 6…