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arXiv · 2003.02964

Stability of Normal Bundles of Space Curves

Izzet Coskun·Eric Larson·Isabel Vogt
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Abstract

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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Izzet Coskun, Eric Larson, Isabel Vogt. 2020-03-05. Stability of Normal Bundles of Space Curves. https://doi.org/10.2140/ant.2022.16.919

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