Polynomial-rational bijections of

Authors:
Krzysztof Kurdyka and Kamil Rusek

Journal:
Proc. Amer. Math. Soc. **102** (1988), 804-808

MSC:
Primary 14E05; Secondary 12D05, 14E07

MathSciNet review:
934846

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Abstract: It is shown in this note that every invertible polynomial transformation of of degree two has a rational inverse defined on the whole space . The same is true for polynomial transformations of higher degrees, satisfying some differential condition which is a real analogue of Jagžev's condition considered in [**3, 4**, and **6**].

The proofs of these statements are based on the Bialynicki-Birula and Rosenlicht surjectivity theorem [**2**] and on standard properties of complex dominant polynomial mappings.

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DOI:
http://dx.doi.org/10.1090/S0002-9939-1988-0934846-2

Article copyright:
© Copyright 1988
American Mathematical Society