Let
![$f(x,y)$](img26.png)
and
![$g(x,y)$](img27.png)
be two non-constant polynomials in two variables with complex coefficients.
We study the relation between the degrees of the resultant of
![$f-u$](img28.png)
and
![$g-v$](img29.png)
with respect to
![$x$](img23.png)
and
![$y$](img30.png)
and the topological degree
![$\deg \varphi$](img31.png)
of the application
![$\varphi = (f,g) :
\mathbb{C}^2 \longrightarrow \mathbb{C}^2.$](img32.png)
The special case
![$\deg \varphi =0$](img33.png)
was considered by Sakkalis
[#!a3!#]. As an application, we give a constructive proof of the known fact, that an injective morphism
![$\varphi:
\mathbb{C}^2 \longrightarrow \mathbb{C}^2$](img34.png)
is actually an automorphism of
![$\mathbb{C}^2$](img35.png)
.