7 papers
Cusps and nodes of Amoeba Contours
Mounir Nisse
We establish new Newton-polygon bounds for the singularities of amoeba contours of smooth plane curves. Our cusp estimate refines the degree-four bound of Lang--Shapiro--Shustin, r…
Singularities of Amoeba Contours
Mounir Nisse
We give explicit real-algebraic equations for computing the singularities of amoeba contours, separating degeneracies of the logarithmic critical locus from coincidences of distinc…
Sparse Bounds for Amoeba Contours
Mounir Nisse
We derive new upper bounds for the real degree of the contour of the amoeba of algebraic curves and hypersurfaces. Our approach refines the Pfaffian method of Lang--Shapiro--Shusti…
Contour Degree of Amoebas of Complete Intersections
Mounir Nisse
We establish the first universal upper bounds for the real degree of the contour of the amoeba of a smooth complete intersection in the algebraic torus. Our approach extends the Pf…
Links represented by phases of algebraic curves
Yen-Kheng Lim, Mounir Nisse
The prime motivation behind this paper is to prove that any torus link can be realized as the union of the one-dimensional connected components of the set of critical values of the…
Phase limit sets of linear spaces and discriminants
Mounir Nisse, Frank Sottile
We show that the closure of the coamoeba of a linear space/hyperplane complement is the union of products of coamoebas of hyperplane complements coming from flags of flats, and rel…