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Stability of Normal Bundles of Space Curves

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posted on 20.06.2022, 15:19 by Izzet CoskunIzzet Coskun, Eric Larson, Isabel Vogt
In this paper, we prove that the normal bundle of a general Brill-Noether space curve of degree $d$ and genus $g \geq 2$ is stable if and only if $(d,g) \not\in \{ (5,2), (6,4) \}$. When $g\leq1$ and the characteristic of the ground field is zero, it is classical that the normal bundle is strictly semistable. We show that this fails in characteristic $2$ for all rational curves of even degree.

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Coskun, I., Larson, E.Vogt, I. (2020). Stability of Normal Bundles of Space Curves. Retrieved from http://arxiv.org/abs/2003.02964v1

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