On the complexification of real-analytic polynomial mappings of $\mathbb{R}^{2}$
Volume 88 / 2006
Annales Polonici Mathematici 88 (2006), 119-125
MSC: Primary 30C99, 30D50, 30C10, 32H02; Secondary 32H50, 32D15, 30C62.
DOI: 10.4064/ap88-2-3
Abstract
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.
