We prove that the normal bundle of a general Brill–Noether space curve of degree $d$ and genus $g\ge 2$ is stable if and only if $(d,g)\notin \{(5,2),(6,4)\}$. When $g\le 1$ and the characteristic of the ground field is zero, it is classical that the normal bundle is strictly semistable. We show that this still holds in positive characteristic except when the characteristic is $2$, the genus is $0$ and the degree is even.

中文翻译：

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空间曲线法线束的稳定性

我们证明了一般 Brill-Noether 空间度曲线的正规丛$d$和属$G\ge 2$是稳定的当且仅当$(d,G)\notin \{(5,2),(6,4)\}$. 什么时候$G\le 1$且地场特性为零，则法线束为严格半稳态是经典的。我们证明这仍然适用于正特征，除非特征是$2$, 属是$0$度数是均匀的。