This note computes the harder-narasimhan filtration of normal bundles in trigonal canonical curves and genus 6 curves.
A trigonal canonical curve lies on a rational normal surface scroll Q ⊂ Pᵍ⁻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 Pᵍ⁻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) studied this question.
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