On the plane section of an integral curve in positive characteristic

Bonacini, Paola

doi:10.1090/S0002-9939-08-09271-X

On the plane section of an integral curve in positive characteristic
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Proc. Amer. Math. Soc. 136 (2008), 2289-2297 Request permission

Abstract:

If $C\subset \mathbb P^3_k$ is an integral curve and $k$ an algebraically closed field of characteristic 0, it is known that the points of the general plane section $C\cap H$ of $C$ are in uniform position. From this it follows easily that the general minimal curve containing $C\cap H$ is irreducible. If char$k=p>0$, the points of $C\cap H$ may not be in uniform position. However, we prove that the general minimal curve containing $C\cap H$ is still irreducible.

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