an:00599125
Zbl 0804.32020
Fourrier, Laurence
Topological classification at infinity of polynomials of two complex variables
FR
C. R. Acad. Sci., Paris, S??r. I 318, No. 5, 461-466 (1994).
00019022
1994
j
32S45 14E15
resolution at infinity; blowing up; topologically conjugate
Let \(f\) be a polynomial of two complex variables, \((f \in C [x,y])\). In order to obtain a topological classification at infinity of polynomials the author constructs a tree of resolution at infinity for \(f\), denoted by \(A_ \infty (f)\). An equivalence relation in the set of trees of resolution at infinity for polynomials is given by blowing up and blowing down. The topological conjugacy at infinity for a pair of two polynomials is also defined. The main result: Two polynomials \(f\) and \(g\) in \(C[x,y]\) are topologically conjugate at infinity if and only if \(A_ \infty (f)\) and \(A_ \infty (g)\) are equivalent.
I.Serb (Cluj-Napoca)