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

Set-theoretic complete intersections


Author: T. T. Moh
Journal: Proc. Amer. Math. Soc. 94 (1985), 217-220
MSC: Primary 14M10; Secondary 14H45
MathSciNet review: 784166
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Abstract: In this article we establish that:

(1) Every monomial curve in $ {\mathbf{P}}_k^n$ is a set-theoretic complete intersection, where $ k$ is a field of characteristic $ p$ (and thus generalize a result of R. Hartshorne [3]).

(2) Let $ k$ be an algebraically closed field of characteristic $ p$ and $ C$ a curve of $ {\mathbf{P}}_k^n$. If there is a linear projection $ \tau :{\mathbf{P}}_k^n \to {\mathbf{P}}_k^2$ with center of $ \tau $ disjoint of $ C$, $ \tau (C)$ is birational to $ C$ and $ \tau (C)$ has only cusps as singularities, then $ C$ is a set-theoretic complete intersection (and thus generalize a result of D. Ferrand [2]).


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DOI: http://dx.doi.org/10.1090/S0002-9939-1985-0784166-1
PII: S 0002-9939(1985)0784166-1
Article copyright: © Copyright 1985 American Mathematical Society