On a plane section of an integral curve in positive characteristic

Details On a plane section of an integral curve in positive characteristic On a plane section of an integral curve in positive characteristic

2010-09-21

arxiv.org/abs/1009.4021v1

Proceedings of the American Mathematical Society Volume 136, Number 7, July 2008, Pages 2289-2297

Mathematics

Algebraic Geometry

Scientific paper

If $C \subset P^3_k$ 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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