The Harder-Narasimhan Filtration of a Trigonal Canonical Curve

Henry Fontana

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arXiv · 2505.14907

The Harder-Narasimhan Filtration of a Trigonal Canonical Curve

Henry Fontana

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Abstract

A trigonal canonical curve lies on a rational normal surface scroll $Q \subset \mathbb{P}^{g-1}$. In this note we use this fact to compute the Harder-Narasimhan filtration of the normal bundle of a general such curve $C$ in $\mathbb{P}^{g-1}$. We also compute the Harder-Narasimhan filtration of the Normal bundle of a general canonical curve of genus $6$.

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Henry Fontana. 2025-05-20. The Harder-Narasimhan Filtration of a Trigonal Canonical Curve. https://arxiv.org/abs/2505.14907

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