作为球商的复射影平面
The complex projective plane as a ball quotient
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中文总结 AI 辅助
研究复射影平面\(\mathbb{P}^2\)作为球商的结构，通过分析分支除子\(D\)是光滑两两正常交叉曲线排列的情况，得出orbifold\((\mathbb{P}^2,D)\)同构于德利涅 - 莫斯托例子或其9度覆盖，推广了庞加莱的\(\mathbb{P}^1\)情形。
中文摘要 AI 辅助
1986年，德利涅和莫斯托构造了一个与复射影平面\(\mathbb{P}^2\)双全纯的球商\(\mathbb{B}^2 / \Gamma\)，其分支轨迹是一个线排列。本文表明，如果\(\mathbb{P}^2\)被实现为一个球商，其分支除子\(D\)是光滑的两两正常交叉曲线的排列，那么orbifold\((\mathbb{P}^2,D)\)同构于德利涅 - 莫斯托的例子或其某个9度覆盖。这种对\(\mathbb{P}^2\)上“球商结构”的分类推广了庞加莱的\(\mathbb{P}^1\)情形。
英文摘要
In 1986, Deligne and Mostow constructed a ball quotient $\mathbb{B}^2 / Γ$ biholomorphic to the complex projective plane $\mathbb{P}^2$ whose branch locus is a line arrangement. In this paper, we show that if $\mathbb{P}^2$ is realized as a ball quotient whose branch divisor $D$ is an arrangement of smooth pairwise normal-crossing curves, then the orbifold $(\mathbb{P}^2,D)$ is isomorphic to either the Deligne-Mostow example or a certain degree 9 cover of it. This classification of "ball quotient structures" on $\mathbb{P}^2$ generalizes the $\mathbb{P}^1$ case due to Poincaré.
