Initial Newton polynomial of the discriminant

Abstract

Let $(f,g):({\mathbb{C}}^2,0)⟶({\mathbb{C}}^2,0)$ be a holomorphic mapping with an isolated zero. We show that the initial Newton polynomial of its discriminant is determined, up to rescalling variables, by the ideals $(f)$ and $(g)$.

References in corpus (1)

• High-school algebra of the theory of dicritical divisors: atypical fibres for special pencils and polynomials