16 papers
From Logarithmic Limit Sets to Algebraicity
Mounir Nisse
We study a converse problem to the theorem of Bergman and Bieri--Groves on logarithmic limit sets of algebraic subvarieties of the complex algebraic torus . We int…
Tropical Degrees and Stable Intersections
Mounir Nisse
We study tropical degree bounds, stable tropical intersections, and tropical Bézout-type estimates through the geometry of Newton polytopes, mixed subdivisions, and lattice indice…
Degree Bounds for Amoeba Contours
Mounir Nisse
We investigate the real algebraic complexity of contours of amoebas associated with algebraic hypersurfaces and complete intersections in complex algebraic tori. Motivated by the f…
Solid Amoebas of Maximally Sparse Polynomials
Mounir Nisse
The topology of amoebas of complex algebraic hypersurfaces is deeply connected to the combinatorics of the Newton polytope and the convex geometry of the Ronkin function. A long-st…
-Maximal Variation of Hodge Structure and Jacobian Rings
Mounir Nisse
We investigate higher--order variation of Hodge structure for families of smooth hypersurfaces and complete intersections through the notion of --maximal variation. Using Griffi…
Maximal Infinitesimal Variation of Hodge Structure for Singular Curves
Mounir Nisse
We study the infinitesimal variation of Hodge structure for families of algebraic curves and extend the classical theory from smooth curves to singular and non--planar settings. Us…