Stability of Normal Bundles of Space Curves

Abstract

In this paper, 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 fails in characteristic $2$ for all rational curves of even degree.

29 pages

References in corpus (1)

• The normal bundle of canonical genus 8 curves