Sharp degree bound for rational proper maps from ${\mathbb{B}}^2$ to ${\mathbb{B}}^4$

Abstract

We prove that every rational proper holomorphic map from ${\mathbb{B}}^2$ to ${\mathbb{B}}^4$ has degree at most $5$, confirming D'Angelo's conjecture in this case. This sharp bound follows from Meylan's degree estimates and an intersection-theoretic argument ruling out degree $6$.

arXiv comment28 pages, comments are welcome