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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
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.

##### 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