Bifurcation sets of real polynomial functions of two variables and Newton polygons

Masaharu Ishikawa, Tat Thang Nguyen, Tiên Son Pham

Research output: Contribution to journalArticle

Abstract

In this paper, we determine the bifurcation set of a real polynomial function of two variables for non-degenerate case in the sense of Newton polygons by using a toric compactification. We also count the number of singular phenomena at infinity, called “cleaving” and “vanishing”, in the same setting. Finally, we give an upper bound of the number of atypical values at infinity in terms of its Newton polygon. To obtain the upper bound, we apply toric modifications to the singularities at infinity successively.

Original languageEnglish
Pages (from-to)1201-1222
Number of pages22
JournalJournal of the Mathematical Society of Japan
Volume71
Issue number4
DOIs
Publication statusPublished - 2019 Jan 1

Keywords

  • Atypical value
  • Bifurcation set
  • Toric compactification

ASJC Scopus subject areas

  • Mathematics(all)

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