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

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概要

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• A. Némethi and A. Zaharia have defined the explicit set for a complex polynomial function f.\bm{C}<SUP>n</SUP>→ \bm{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.

• 社団法人 日本数学会の論文

著者

• Ishikawa Masaharu

  Graduate School Of Mathematical Sciences The University Of Tokyo

関連論文

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

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