#### Vol. 16, No. 4, 2022

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Stability of normal bundles of space curves

### Izzet Coskun, Eric Larson and Isabel Vogt

Vol. 16 (2022), No. 4, 919–953
##### 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 $\left(d,g\right)\notin \left\{\left(5,2\right),\left(6,4\right)\right\}$. 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.

##### Keywords
normal bundle, Brill–Noether curve, stability
##### Mathematical Subject Classification
Primary: 14H50, 14H60
Secondary: 14B99
##### Milestones
Received: 27 August 2020
Revised: 14 May 2021
Accepted: 5 August 2021
Published: 5 August 2022
##### Authors
 Izzet Coskun Department of Mathematics, Statistics, and Computer Science University of Illinois at Chicago Chicago, IL United States Eric Larson Department of Mathematics University of Washington Seattle, WA United States Department of Mathematics Brown University Providence, RI United States Isabel Vogt Department of Mathematics University of Washington Seattle, WA United States Department of Mathematics Brown University Providence, RI United States