Tetragonal Canonical Curves

We compute the Harder-Narasimhan Filtration of the normal bundle $N_{C/\mathbb{P}^{g-1}}$ where $C$ is a general tetragonal canonical curve of genus $g$.

💡 Research Summary

In this paper the author determines the Harder–Narasimhan (HN) filtration of the normal bundle (N_{C/\mathbb{P}^{g-1}}) for a general tetragonal (i.e. (g^1_4)) canonical curve (C) of genus (g). The study builds on the well‑known fact that a tetragonal canonical curve lies on a three‑dimensional rational normal scroll (Q\subset\mathbb{P}^{g-1}). By a result of Schreyer (Section 6 of