The normal bundle of canonical genus 8 curves

TL;DR

This paper proves that the normal bundle of a general canonical genus 8 curve is stable, supporting a broader conjecture that such stability holds for all high-genus canonical curves.

Contribution

It establishes the stability of the normal bundle for genus 8 curves using Mukai's description, advancing the conjecture for all genus g ≥ 7.

Findings

Normal bundle of general genus 8 curves is stable.

Supports the conjecture for stability of normal bundles in higher genus.

Provides evidence for the stability conjecture beyond genus 8.

Abstract

We study the stability of the normal bundle of canonical genus $8$ curves and prove that on a general curve the bundle is stable. The proof rests on Mukai's description of these curves as linear sections of a Grassmannian $\mathrm{G}(2,6)$. This is the next case of a conjecture by M. Aprodu, G. Farkas, and A. Ortega: the general canonical curve of every genus $g \geq 7$ should have stable normal bundle. We also give some more evidence for this conjecture in higher genus.