English

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

Complex Variables 2007-10-26 v2

Abstract

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.

Keywords

Cite

@article{arxiv.0710.4597,
  title  = {A criterion for a proper rational map to be equivalent to a proper polynomial map},
  author = {Xiaojun Huang and Shanyu Ji and Yuan Zhang},
  journal= {arXiv preprint arXiv:0710.4597},
  year   = {2007}
}

Comments

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

R2 v1 2026-06-21T09:35:45.431Z