Loose edges and factorization theorems

Abstract

Let $R$ be a regular local ring with maximal ideal $\mathfrak{m}$. We consider elements $f\in R$ such that their Newton polyhedron has a loose edge. We show that if the symbolic restriction of $f$ to such an edge is a product of two coprime polynomials, then $f$ factorizes in the $\mathfrak{m}$-adic completion.

15 pages, 6 figures, this articles merges and supersedes arxiv:1807.04944 and arxiv:1808.09587

References in corpus (1)

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