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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Projective surfaces over a finite field

Authors: Roger Wiegand and William Krauter
Journal: Proc. Amer. Math. Soc. 83 (1981), 233-237
MSC: Primary 14J99
MathSciNet review: 624904
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Abstract: Let $ k$ be the algebraic closure of a finite field, and let $ X$ be an irreducible projective surface over $ k$. Let $ C$ be a curve on $ X$, and let $ \Omega $ be a finite set of closed points of $ X$ meeting each irreducible component of $ X$. We prove that there is an irreducible curve on $ X$ whose set-theoretic intersection with $ C$ is $ \Omega $. Using this theorem we characterize $ {\mathbf{P}}_k^2$ as a topological space, and we show that for any two irreducible plane curves $ C$, $ C'$ there is a homeomorphism from $ {\mathbf{P}}_k^2$ onto itself taking $ C$ onto $ C'$.

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Article copyright: © Copyright 1981 American Mathematical Society

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