Nondegeneracy and Discrete Models

On Nondegeneracy of Curves

We study the conditions under which an algebraic curve can be modelled by a Laurent polynomial that is nondegenerate with respect to its Newton polytope. We prove that every curve of genus g ≤ 4 over an algebraically closed field is nondegenerate in the above sense. More generally, let M g be the locus of nondegenerate curves inside the moduli space of curves of genus g ≥ 2. Then we show that d...

Generic nondegeneracy in convex optimization

We show that minimizers of convex functions subject to almost all linear perturbations are nondegenerate. An analogous result holds more generally, for lower-C2 functions.

Addenda and Errata: on Nondegeneracy of Curves

(1) Beginning of Section 5: We write that every genus g hyperelliptic curve over a perfect field k is birationally equivalent (over k) to a curve of the form y + q(x)y = p(x) where p(x), q(x) ∈ k[x] satisfy 2 deg q(x) ≤ deg p(x) and deg p(x) ∈ {2g + 1, 2g + 2}. This is false for (and only for) k = F2. Namely, this will fail for any hyperelliptic curve C over k = F2 for which the degree 2 morphi...

Nondegeneracy of Polyhedra and Linear Programs

This paper deals with nondegeneracy of polyhedra and linear programming (LP) problems. We allow for the possibility that the polyhedra and the feasible polyhedra of the LP problems under consideration be non-pointed. (A polyhedron is pointed if it has a vertex.) With respect to a given polyhedron, we consider two notions of nondegeneracy and then provide several equivalent characterizations for...

Remarks on Nondegeneracy in Mixedsemidefinite { Quadratic