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/