A geometric approach to the Jacobian Conjecture in ℂ²
Volume 55 / 1991
Annales Polonici Mathematici 55 (1991), 95-101
DOI: 10.4064/ap-55-1-95-101
Abstract
We consider polynomial mappings (f,g) of ℂ² with constant nontrivial jacobian. Using the Riemann-Hurwitz relation we prove among other things the following: If g - c (resp. f - c) has at most two branches at infinity for infinitely many numbers c or if f (resp. g) is proper on the level set $g^{-1}(0)$ (resp. $f^{-1}(0)$), then (f,g) is bijective.
