We give a simple algebraic condition on the leading homogeneous term of a polynomial mapping from ℝ² into ℝ² which is equivalent to the fact that the complexification of this mapping can be extended to a polynomial endomorphism of ℂℙ². We also prove that this extension acts on ℂℙ²∖ℂ² as a quotient of finite Blaschke products.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ap88-2-3,
author = {Ewa Ligocka},
title = {On the complexification of real-analytic polynomial mappings of $\mathbb{R}$$^2$},
journal = {Annales Polonici Mathematici},
volume = {89},
year = {2006},
pages = {119-125},
zbl = {1129.30018},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap88-2-3}
}
Ewa Ligocka. On the complexification of real-analytic polynomial mappings of ℝ². Annales Polonici Mathematici, Tome 89 (2006) pp. 119-125. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap88-2-3/