On bifurcation points of a complex polynomial

被引:4
作者
Jelonek, Z [1 ]
机构
[1] Polish Acad Sci, Inst Matemat, PL-31027 Krakow, Poland
关键词
polynomial mapping; fibration; bifurcation points; the set of points over which a polynomial mapping is not proper; VARIABLES;
D O I
10.1090/S0002-9939-02-06822-3
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
Let f : C-n --> C be a polynomial of degree d. Assume that the set (K) over tilde (infinity)(f) = {y is an element of C : there is a sequence x(l) --> infinity s.t. f(x(l)) --> y and parallel todf(x(l))parallel to --> 0} is finite. We prove that the set (K) over tilde (f) - K-o(f) boolean OR (K) over tilde (infinity)(f) of generalized critical values of f (hence in particular the set of bifurcation points of f) has at most (d - 1)(n) points. Moreover, #(K) over tilde (infinity)(f) < (d - 1)(n-1). We also compute the set (K) over tilde (f) effectively.
引用
收藏
页码:1361 / 1367
页数:7
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