A non-zero constant Jacobian polynomial map F=(P,Q):ℂ² → ℂ² has a polynomial inverse if the component P is a simple polynomial, i.e. its regular extension to a morphism p:X → ℙ¹ in a compactification X of ℂ² has the following property: the restriction of p to each irreducible component C of the compactification divisor D = X-ℂ² is of degree 0 or 1.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ap93-3-5,
author = {Nguyen Van Chau},
title = {Plane Jacobian conjecture for simple polynomials},
journal = {Annales Polonici Mathematici},
volume = {93},
year = {2008},
pages = {247-251},
zbl = {1137.14048},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap93-3-5}
}
Nguyen Van Chau. Plane Jacobian conjecture for simple polynomials. Annales Polonici Mathematici, Tome 93 (2008) pp. 247-251. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap93-3-5/