Stability of normal bundles of Brill--Noether curves in ℙ⁴

2026/08/02 by Izzet Coskun, Eric Jovinelly, Eric Larson
Mathematics · #math.AG #msc:14H60

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arxiv created 2026/08/02 · arxiv updated 2026/08/04

Abstract

We prove that a general Brill--Noether curve C of genus g ≥ 2 and degree d in ℙ⁴ has stable normal bundle N_C if and only if (g, d) ∉ \(2,6), (3,7), (5,8), (6,9), (7,10)\. Moreover, N_C is strictly semistable if (g, d) ∈ \(3, 7), (5, 8)\, and is unstable if (g, d) ∈ \(2, 6), (6, 9), (7, 10)\. Our results are valid in any characteristic. Along the way, we also generalize previous results of Larson--Vogt on interpolation for N_C(-1), from characteristic zero to arbitrary characteristic.

Citations

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