A geometric approach to the Jacobian Conjecture in ℂ²
Ludwik M. Drużkowski
Annales Polonici Mathematici, Tome 55 (1991), p. 95-101 / Harvested from The Polish Digital Mathematics Library
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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.

Publié le : 1991-01-01
EUDML-ID : urn:eudml:doc:262260 
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     author = {Ludwik M. Dru\.zkowski},
     title = {A geometric approach to the Jacobian Conjecture in $\mathbb{C}$$^2$},
     journal = {Annales Polonici Mathematici},
     volume = {55},
     year = {1991},
     pages = {95-101},
     zbl = {0772.14006},
     language = {en},
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Ludwik M. Drużkowski. A geometric approach to the Jacobian Conjecture in ℂ². Annales Polonici Mathematici, Tome 55 (1991) pp. 95-101. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-apmv55z1p95bwm/

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