On the complexification of real-analytic polynomial mappings of
$\mathbb{R}^{2}$
Annales Polonici Mathematici, Volume 88 (2006) no. 2, pp. 119-125
See the original article notice from the Institute of Mathematics Polish Academy of Sciences source
We give a simple algebraic condition on the leading homogeneous term
of a polynomial mapping from $\mathbb{R}^{2}$ into $\mathbb{R}^{2}$
which is equivalent to the fact that the complexification of this
mapping can be extended to a polynomial endomorphism of $\mathbb{C}\mathbb{P}^{2}$.
We also prove that this extension acts on $\mathbb{C}\mathbb{P}^{2}\setminus\mathbb{C}^{2}$
as a quotient of finite Blaschke products.
Keywords:
simple algebraic condition leading homogeneous term polynomial mapping mathbb mathbb which equivalent the complexification mapping extended polynomial endomorphism mathbb mathbb prove extension acts mathbb mathbb setminus mathbb quotient finite blaschke products
Author's affiliations:
Ewa Ligocka 1
Ewa Ligocka. On the complexification of real-analytic polynomial mappings of
$\mathbb{R}^{2}$. Annales Polonici Mathematici, Volume 88 (2006) no. 2, pp. 119-125. doi: 10.4064/ap88-2-3
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title = {On the complexification of real-analytic polynomial mappings of
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journal = {Annales Polonici Mathematici},
pages = {119--125},
year = {2006},
volume = {88},
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doi = {10.4064/ap88-2-3},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/ap88-2-3/}
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AU - Ewa Ligocka
TI - On the complexification of real-analytic polynomial mappings of
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JO - Annales Polonici Mathematici
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VL - 88
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UR - http://geodesic.mathdoc.fr/articles/10.4064/ap88-2-3/
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