Description |
Let $\phi = (f,g): C^2 \rightarrow C^2$ be a polynomial map of the plane over the field C of complex numbers with its Jacobian nonzero constant. The Jacobian conjecture asserts that $\phi$ must be an automorphism. We say that a point $P_infty \in P^2 \C^2$ of the complex projective plane P^2 is a `quasifinite' (w.r.t. \phi)$ if there exists a sequence
$\{P_i\}$ in $C^2 \in P^2$ converging
to $P_\infty$ such that the image $\{\phi(P_i)\}$ converges to a point in
C^2. In this talk I will show that the conjecture holds if any only if there is no quasifinite point.
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