A+ CATEGORY SCIENTIFIC UNIT

Analytically principal part of polynomials at infinity

Volume 117 / 2016

Nguyễn Thảo Nguyên Bùi, Tiến-Sơn Phạm 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.

Authors

  • Nguyễn Thảo Nguyên BùiDepartment of Pedagogy
    University of Dalat
    1 Phu Dong Thien Vuong
    Dalat, Vietnam
    e-mail
  • Tiến-Sơn PhạmInstitute of Research and Development
    Duy Tan University, K7/25
    Quang Trung
    Danang, Vietnam
    and
    Department of Mathematics
    University of Dalat
    1 Phu Dong Thien Vuong
    Dalat, Vietnam
    e-mail

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