The normal bundle of a general canonical curve of genus at least 7 is semistable

Izzet Coskun; Eric Larson; Isabel Vogt

doi:10.4171/jems/1476

JournalsjemsVol. 28, No. 1pp. 333–358

The normal bundle of a general canonical curve of genus at least 7 is semistable

Izzet Coskun
University of Illinois at Chicago, USA
Eric Larson
Brown University, Providence, USA
Isabel Vogt
Brown University, Providence, USA

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Abstract

Let $C$ be a general canonical curve of genus $g$ defined over an algebraically closed field of arbitrary characteristic. We prove that if $g \in / {4, 6}$ , then the normal bundle of $C$ is semistable. In particular, if $g \equiv 1$ or $3 (mod 6)$ , then the normal bundle is stable.

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Izzet Coskun, Eric Larson, Isabel Vogt, The normal bundle of a general canonical curve of genus at least 7 is semistable. J. Eur. Math. Soc. 28 (2026), no. 1, pp. 333–358

DOI 10.4171/JEMS/1476