Topological classification at infinity of polynomials of two complex variables. (Classification topologique à l’infini des polynômes de deux variables complexes.) (French. Abridged English version) Zbl 0804.32020

Fourrier, Laurence

C. R. Acad. Sci., Paris, Sér. I 318, No. 5, 461-466 (1994).

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.

Reviewer: I.Serb (Cluj-Napoca)

MSC:

32S45	Modifications; resolution of singularities (complex-analytic aspects)
14E15	Global theory and resolution of singularities (algebro-geometric aspects)

Keywords:

resolution at infinity; blowing up; topologically conjugate