Analytically principal part of polynomials at infinity
Volume 117 / 2016
Annales Polonici Mathematici 117 (2016), 259-268
MSC: 14P10, 32S05, 58C27, 58K05.
DOI: 10.4064/ap3560-4-2016
Published online: 2 August 2016
Abstract
Let $f \colon \mathbb{K}^n \rightarrow \mathbb{K}$ be a polynomial function, where $\mathbb{K} := \mathbb{R}$ or $\mathbb{C}.$ We give, in terms of the Newton boundary at infinity of $f,$ a sufficient condition for a deformation of $f$ to be analytically (smoothly in the case $\mathbb{K} := \mathbb{C}$) trivial at infinity.
