Do most polynomials generate a prime ideal?
arXiv:1509.02050 · doi:10.1016/j.jalgebra.2016.03.050
Abstract
For which monomial supports do most polynomials generate a prime ideal? We give necessary and sufficient conditions for the radical of the ideal to be prime over an algebraically closed field. In characteristic zero, the same conditions give primeness. As an application we show that under the same combinatorial conditions on Newton polytopes, the stable intersection of tropical hypersurfaces is connected through codimension one.
6 pages. Minor changes from version 2. Removed example (5'). Added an open problem section