A criterion for a proper rational map to be equivalent to a proper polynomial map

Details A criterion for a proper rational map to be equivalent to a proper polynomial map A criterion for a proper rational map to be equivalent to a proper polynomial map

2007-10-25

arxiv.org/abs/0710.4597v2

Mathematics

Complex Variables

13 pages. Dedicated to Professor J. Kohn on the occasion of his 75th birthday

Scientific paper

In this paper, we give an explicit criterion when a rational holomorphic map between balls is equivalent to a polynomial holomorphic map. Making use of this criterion, we show that any proper rational holomorphic map from B^2 into B^N of degree two is equivalent to a polynomial holomorphic map; we also construct rational holomorphic maps of degree 3 that are almost linear but are not equivalent to polynomial holomorphic maps.

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