The normal bundle of canonical genus 8 curves

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 $g\ge 7$ should have stable normal bundle. We also give some more evidence for this conjecture in higher genus.

19 pages. Comments are welcome. v2: Added an address and simplified the proofs of lemmas B.3 and B.4

Cited by in corpus (2)

• Stability of Normal Bundles of Space Curves
• On the Normal Sheaf of Gorenstein Curves