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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
DOI: https://doi.org/10.1090/S0002-9939-1985-0784166-1
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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Article copyright: © Copyright 1985 American Mathematical Society