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arXiv · 2308.13756

On The Cohomology of $N_C(-2)$ in Positive Characteristic

Eric Larson
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Abstract

Let $C \subset \mathbb{P}^3$ be a general Brill--Noether curve. A classical problem is to determine when $H^0(N_C(-2)) = 0$, which controls the quadric section of $C$. So far this problem has only been solved in characteristic zero, in which case $H^0(N_C(-2)) = 0$ with finitely many exceptions. In this note, we extend these results to positive characteristic, uncovering a wealth of new exceptions in characteristic 2.

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Eric Larson. 2023-08-26. On The Cohomology of $N_C(-2)$ in Positive Characteristic. https://arxiv.org/abs/2308.13756

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