Geometry of Factorization Identities for Discriminants

Abstract

Let Δn be the discriminant of a general polynomial of degree n and $$\mathcal{N}$$ be the Newton polytope of Δn. We give a geometric proof of the fact that the truncations of Δn to faces of $$\mathcal{N}$$ are equal to products of discriminants of lesser n degrees. The proof is based on the blow-up property of the logarithmic Gauss map for the zero set of Δn.