The bifurcation set of a complex polynomial function of two variables and the newton polygons of singularities at infinity

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6 Citations (Scopus)

Abstract

A. Némethi and A. Zaharia have defined the explicit set for a complex polynomial function f: Cn → C and conjectured that the bifurcation set of the global fibration of f is given by the union of the set of critical values and the explicit set of f. They have proved only the case n = 2 and f is Newton non-degenerate. In the present paper we will prove this for the case n = 2, containing the Newton degenerate case, by using toric modifications and give an expression of the bifurcation set of f in the words of Newton polygons.

Original languageEnglish
Pages (from-to)161-196
Number of pages36
JournalJournal of the Mathematical Society of Japan
Volume54
Issue number1
DOIs
Publication statusPublished - 2002 Jan 1
Externally publishedYes

Fingerprint

Bifurcation Set
Newton Polygon
Complex Polynomials
Complex Functions
Polynomial function
Infinity
Singularity
Fibration
Critical value
Union

Keywords

  • Bifurcation set
  • Complex polynomial functions
  • Newton polygons
  • Singularities at infinity
  • Toric modifications

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

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AB - A. Némethi and A. Zaharia have defined the explicit set for a complex polynomial function f: Cn → C and conjectured that the bifurcation set of the global fibration of f is given by the union of the set of critical values and the explicit set of f. They have proved only the case n = 2 and f is Newton non-degenerate. In the present paper we will prove this for the case n = 2, containing the Newton degenerate case, by using toric modifications and give an expression of the bifurcation set of f in the words of Newton polygons.

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