AI 中文总结
本文研究P⁴中Brill–Noether曲线的法丛稳定性，明确了不同亏格与次数组合下法丛的稳定、严格半稳定或不稳定状态，并将Larson–Vogt的相关插值结果推广至任意特征。
AI 中文摘要
我们证明：P⁴中亏格g≥2、次数为d的一般Brill–Noether曲线C，其法丛N_C稳定当且仅当(g,d)∉{(2,6),(3,7),(5,8),(6,9),(7,10)}；当(g,d)∈{(3,7),(5,8)}时，N_C严格半稳定；当(g,d)∈{(2,6),(6,9),(7,10)}时，N_C不稳定。所得结果在任意特征下均成立。同时，我们还将Larson–Vogt关于N_C(-1)插值的结果，从特征零推广到了任意特征。
英文摘要
We prove that a general Brill--Noether curve $C$ of genus $g \geq 2$ and degree $d$ in $\mathbb{P}^4$ has stable normal bundle $N_C$ if and only if $$(g, d) \notin \{(2,6), (3,7), (5,8), (6,9), (7,10)\}.$$ Moreover, $N_C$ is strictly semistable if $(g, d) \in \{(3, 7), (5, 8)\}$, and is unstable if $(g, d) \in \{(2, 6), (6, 9), (7, 10)\}$. Our results are valid in any characteristic. Along the way, we also generalize previous results of Larson--Vogt on interpolation for $N_C(-1)$, from characteristic zero to arbitrary characteristic.
