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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On the plane section of an integral curve in positive characteristic


Author: Paola Bonacini
Journal: Proc. Amer. Math. Soc. 136 (2008), 2289-2297
MSC (2000): Primary 14H50; Secondary 13D40
Published electronically: March 19, 2008
MathSciNet review: 2390494
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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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Additional Information

Paola Bonacini
Affiliation: Dipartimento di Matematica e Informatica, Università degli Studi di Catania, Viale A. Doria 6, 95125 Catania, Italy
Email: bonacini@dmi.unict.it

DOI: http://dx.doi.org/10.1090/S0002-9939-08-09271-X
PII: S 0002-9939(08)09271-X
Keywords: Integral curve, plane section, minimal curve, positive characteristic
Received by editor(s): July 26, 2006
Received by editor(s) in revised form: February 19, 2007
Published electronically: March 19, 2008
Communicated by: Ted Chinburg
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.