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]).

References [Enhancements On Off] (What's this?)

  • [1] R. C. Cowsik and M. V. Nori, Affine curves in characteristic 𝑝 are set theoretic complete intersections, Invent. Math. 45 (1978), no. 2, 111–114. MR 0472835
  • [2] Daniel Ferrand, Set-theoretical complete intersections in characteristic 𝑝>0, Algebraic geometry (Proc. Summer Meeting, Univ. Copenhagen, Copenhagen, 1978), Lecture Notes in Math., vol. 732, Springer, Berlin, 1979, pp. 82–89. MR 555692
  • [3] Robin Hartshorne, Complete intersections in characteristic 𝑝>0, Amer. J. Math. 101 (1979), no. 2, 380–383. MR 527998, 10.2307/2373984

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Article copyright: © Copyright 1985 American Mathematical Society