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 indices…
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…
Equisingular Deformations of Curves and Surfaces in Threefolds
Mounir Nisse
We study equisingular deformation problems for curves and surfaces in algebraic families, with particular emphasis on situations where nodal behavior is no longer generic. Extendin…
Logarithmic Equigeneric Smoothing and Maximal Nodal Degenerations
Mounir Nisse
We study equisingular deformation problems for curves and surfaces in algebraic families, with particular emphasis on situations where nodal behavior is no longer generic. Extendin…
Logarithmic geometry and Infinitesimal Hodge Theory
Mounir Nisse
This paper develops a systematic approach to infinitesimal variations of Hodge structure for singular and equisingular families by means of logarithmic geometry and residue theory.…
Residues and Infinitesimal Torelli for Equisingular Curves
Mounir Nisse
We study infinitesimal Torelli problems and infinitesimal variations of Hodge structure for families of curves arising in singular and extrinsically constrained geometric settings.…
Infinitesimal Variations of Hodge Structure for Singular Curves I
Mounir Nisse
We study the infinitesimal variation of Hodge structure associated with families of reduced algebraic curves with singularities. The analysis applies to curves beyond the nodal cas…
Maximal Variation in the Moduli of Curves
Mounir Nisse
We introduce and study the maximal-variation locus in families and moduli spaces of projective curves, defined via conductor-level balancing of meromorphic differentials on the nor…
Residue Balancing on Singular Curves
Mounir Nisse
This paper investigates residue maps and their spanning properties for singular algebraic curves, with particular emphasis on three interconnected themes: the \emph{scheme--theoret…
On infinitesimal deformations of singular varieties III
Mounir Nisse
We study the affine cone over a reducible nodal curve obtained by gluing three projective lines along three pairs of points to form a connected curve of arithmetic genus \(1\).…
On infinitesimal deformations of singular varieties II
Mounir Nisse
The deformation theory of affine cones over polarized projective varieties, initiated by Pinkham and further developed by Schlessinger and Wahl, is central to the study of singular…
On infinitesimal deformations of singular varieties I
Mounir Nisse
The deformation theory of singular varieties plays a central role in understanding the geometry and moduli of algebraic varieties. For a variety with possibly singular points,…