13 citations · 32 across the 22 of their papers we have counts for
5 papers · 1 filter
Higher convexity for complements of tropical varieties
Mounir Nisse, Frank Sottile
We consider Gromov's homological higher convexity for complements of tropical varieties, establishing it for complements of tropical hypersurfaces and curves, and for nonarchimedea…
A tropical characterization of complex analytic varieties to be algebraic
Farid Madani, Lamine Nisse, Mounir Nisse
In this paper we study a -dimensional analytic subvariety of the complex algebraic torus. We show that if its logarithmic limit set is a finite rational -dimensional sphe…
Higher convexity of coamoeba complements
Mounir Nisse, Frank Sottile
We show that the complement of the coamoeba of a variety of codimension k+1 is k-convex, in the sense of Gromov and Henriques. This generalizes a result of Nisse for hypersurface c…
Amoeba finite basis of solutions to a system of polynomials in variables
Mounir Nisse
We show that the amoeba of a complex algebraic variety defined as the solutions to a generic system of polynomials in variables has a finite basis. In other words, it is th…
Amoeba finite basis does not exist in general
Mounir Nisse
We show that the amoeba of a generic complex algebraic variety of codimension do not have a finite basis. In other words, it is not the intersection of finitely many hypers…