In certain cases the invertibility of a polynomial map F = (P,Q): ℂ²→ ℂ² can be characterized by the irreducibility and the rationality of the curves aP+bQ = 0, (a:b) ∈ ℙ¹.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ap101-1-5,
author = {Nguyen Van Chau},
title = {Pencils of irreducible rational curves and plane Jacobian conjecture},
journal = {Annales Polonici Mathematici},
volume = {101},
year = {2011},
pages = {47-53},
zbl = {1230.14094},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap101-1-5}
}
Nguyen Van Chau. Pencils of irreducible rational curves and plane Jacobian conjecture. Annales Polonici Mathematici, Tome 101 (2011) pp. 47-53. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap101-1-5/