Stability of normal bundles of space curves

Coskun, Izzet; Larson, Eric; Vogt, Isabel

doi:10.2140/ant.2022.16.919

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Stability of normal bundles of space curves

Izzet Coskun, Eric Larson and Isabel Vogt

Vol. 16 (2022), No. 4, 919–953

DOI: 10.2140/ant.2022.16.919

Abstract

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 $(d, g) \notin {(5, 2), (6, 4)}$ . When $g \leq 1$ and the characteristic of the ground field is zero, it is classical that the normal bundle is strictly semistable. We show that this still holds in positive characteristic except when the characteristic is $2$ , the genus is $0$ and the degree is even.

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Keywords

normal bundle, Brill–Noether curve, stability

Mathematical Subject Classification

Primary: 14H50, 14H60

Secondary: 14B99

Milestones

Received: 27 August 2020

Revised: 14 May 2021

Accepted: 5 August 2021

Published: 5 August 2022

Authors

Izzet Coskun
Department of Mathematics, Statistics, and Computer Science University of Illinois at Chicago Chicago, IL United States

Eric Larson
Department of Mathematics University of Washington Seattle, WA United States	Department of Mathematics Brown University Providence, RI United States

Isabel Vogt
Department of Mathematics University of Washington Seattle, WA United States	Department of Mathematics Brown University Providence, RI United States

Vol. 16, No. 4, 2022