A geometrical approach to the Jacobian conjecture for \(n=2\). (English) Zbl 1128.14301

Summary: Let us recall the Jacobian conjecture: “Jacobian Conjecture. Let \(F: \mathbb C^n \to \mathbb C^n\) be a polynomial map. Suppose that, for every point \(x \in \mathbb C^n\), the derivative \(F' (x)\) is invertible. Then the map \(F\) is invertible.”
In this lecture we describe a geometrical approach to this conjecture when \(n=2\).


14E07 Birational automorphisms, Cremona group and generalizations
13F20 Polynomial rings and ideals; rings of integer-valued polynomials
14E05 Rational and birational maps
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