从 $\mathbb B^2$ 到 $\mathbb B^4$ 的有理真映射的锐利次数界
Sharp degree bound for rational proper maps from $\mathbb B^2$ to $\mathbb B^4$
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中文总结 AI 辅助
本文证明了从二维复球到四维复球的有理真映射的D'Angelo次数猜想，通过特征数方法确立五次为锐利上界。
中文摘要 AI 辅助
我们证明了从 $\mathbb{B}^2$ 到 $\mathbb{B}^4$ 的有理真全纯映射的 D'Angelo 次数猜想，确立了五次这一锐利次数界。假设相反，存在一个六次有理真映射。我们为该映射关联一个特征数，用以度量其射影微分数据的退化程度。一个全局相交理论计算精确确定了该数，而沿退化轨迹的局部分析则得出同一量的严格更大的下界。这一矛盾排除了六次情形，从而证明了所猜想的次数界。
英文摘要
We prove D'Angelo's degree conjecture for rational proper holomorphic maps from $\mathbb{B}^2$ to $\mathbb{B}^4$, establishing the sharp degree bound of five. Suppose, to the contrary, that a rational proper map of degree six exists. We associate to the map a characteristic number measuring the degeneracy of its projective differential data. A global intersection-theoretic computation determines this number exactly, while a local analysis along the degeneracy locus yields a strictly larger lower bound for the same quantity. This contradiction excludes degree six and proves the conjectured bound.
发表机构
- School of Mathematics and Statistics, Wuhan University（武汉大学数学与统计学院）
机构由 AI 辅助整理，请以论文原文为准。
