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## On the complexification of real-analytic polynomial mappings of $\mathbb{R}^{2}$

### Tom 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

#### Streszczenie

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.

#### Autorzy

• Ewa LigockaInstitute of Mathematics
Department of Mathematics, Computer Science and Mechanics
Warsaw University
Banacha 2
02-097 Warszawa, Poland
e-mail

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