Almost-toric Hypersurfaces

TL;DR

This paper studies almost-toric hypersurfaces, characterizes their Newton polytopes, and introduces an algorithm to compute their implicit equations efficiently.

Contribution

It provides a detailed description of the Newton polytope for almost-toric hypersurfaces and develops a novel algorithm for implicitization.

Findings

Newton polytope of almost-toric hypersurfaces characterized

Algorithm for implicit equation computation proposed

Enhanced understanding of hypersurface parameterizations

Abstract

An almost-toric hypersurface is parameterized by monomials multiplied by polynomials in one extra variable. We determine the Newton polytope of such a hypersurface, and apply this to give an algorithm for computing the implicit equation.