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

被引：6

作者：

Ishikawa, M ^{[1
]}

机构：

[1] Univ Tokyo, Grad Sch Math Sci, Meguro Ku, Tokyo 1538914, Japan

来源：

JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN | 2002年 / 54卷 / 01期

关键词：

complex polynomial functions; bifurcation set; singularities at infinity; Newton polygons; toric modifications;

D O I：

10.2969/jmsj/1191593959

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

A. Nemethi and A. Zaharia have defined the explicit set for a complex polynomial function f: C-n --> 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.

引用

页码：161 / 196

页数：36