Stability of normal bundles of space curves

Abstract

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.