On a plane section of an integral curve in positive characteristic

Paola Bonacini

On a plane section of an integral curve in positive characteristic

Algebraic Geometry 2010-09-22 v1

Authors: Paola Bonacini

Abstract

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.

Keywords

integral curve plane section positive characteristic uniform position minimal curve irreducibility

Cite

@article{arxiv.1009.4021,
  title  = {On a plane section of an integral curve in positive characteristic},
  author = {Paola Bonacini},
  journal= {arXiv preprint arXiv:1009.4021},
  year   = {2010}
}

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