A criterion for a proper rational map to be equivalent to a proper polynomial map
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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.
13 pages. Dedicated to Professor J. Kohn on the occasion of his 75th birthday
13 pages. Dedicated to Professor J. Kohn on the occasion of his 75th birthday