Newton Polyhedra and Factorial Rings

Determinantal singularities and Newton polyhedra

We introduce so called resultantal singularities (Definitions 5.1 and 8.1), whose study in terms of Newton polyhedra unifies the tasks A and B to a certain extent. In particular, this provides new formulations and proofs for a number of well known results (see, for example, Theorem 5.7 related to task A and Corollary 4.6 related to task B). As an application, we study basic topological invarian...

Newton Polyhedra, a New Formula for Mixed Volume, Product of Roots of a System of Equations

We generalize Vieta formula for the product of roots of a polynomial to the multidimensional case. We compute in the group (C∗)n the product of all roots of a system of n polynomial equations with sufficiently general Newton polyhedra. We present two different formulas for this product. In the first formula we use the so called Parshin symbols, in the second formula we use derivatives of the mi...

Newton polyhedra and Poisson structures from certain linear Hamiltonian circle actions

In this paper we first describe the geometry of the Newton polyhedra of polynomials invariant under certain linear Hamiltonian circle actions. From the geometry of the polyhedra, various Poisson structures on the orbit spaces of the actions are derived and Poisson embeddings into model spaces, for the orbit spaces, are constructed. The Poisson structures, on respective source and model space, a...

4 N ov 2 00 6 Elimination theory and Newton polyhedra

The Foldings of a Square to Convex Polyhedra

The structure of the set of all convex polyhedra foldable from a square is detailed. It is proved that five combinatorially distinct nondegenerate polyhedra, and four different flat polyhedra, are realizable. All the polyhedra are continuously deformable into each other, with the space of polyhedra having the topology of four connected rings.