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Sharp degree bound for rational proper maps from 𝔹2 to 𝔹4
Abstract
We prove that every rational proper holomorphic map from 𝔹2 to 𝔹4 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 $6$.
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BibTeX
@misc{hu2026sharp,
title = {{Sharp degree bound for rational proper maps from $\mathbb B^2$ to $\mathbb B^4$}},
author = {Tianzhi Hu and Mai Shi and Pingsan Yuan},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.15698},
eprint = {2609.15698},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.15698},
}
RIS
TY - UNPB
TI - Sharp degree bound for rational proper maps from 𝔹^2 to 𝔹^4
AU - Tianzhi Hu
AU - Mai Shi
AU - Pingsan Yuan
PY - 2026
DA - 2026/10/12
PB - arXiv
DO - 10.48550/arxiv.2609.15698
UR - https://arxiv.org/abs/2609.15698
AB - We prove that every rational proper holomorphic map from 𝔹^2 to 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 $6$.
ER -