S. Jadiba: Résultant et degré topologique en dimension deux, p.219-231

Abstract:

Let $f(x,y)$ and $g(x,y)$ be two non-constant polynomials in two variables with complex coefficients. We study the relation between the degrees of the resultant of $f-u$ and $g-v$ with respect to $x$ and $y$ and the topological degree $\deg \varphi$ of the application $\varphi = (f,g) : \mathbb{C}^2 \longrightarrow \mathbb{C}^2.$ The special case $\deg \varphi =0$ was considered by Sakkalis [#!a3!#]. As an application, we give a constructive proof of the known fact, that an injective morphism $\varphi: \mathbb{C}^2 \longrightarrow \mathbb{C}^2$ is actually an automorphism of $\mathbb{C}^2$.

Key Words: Résultant, degré topologique, automorphismes affines.

2000 Mathematics Subject Classification: Primary: 14R10, 14R15,
Secondary: 14E22.

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