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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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A characterization of complete intersection curves in $\textbf {P}^ 3$
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by Rosario Strano PDF
Proc. Amer. Math. Soc. 104 (1988), 711-715 Request permission

Abstract:

We prove the following theorem. Let $C \subset {{\mathbf {P}}^3}$ be a reduced and irreducible curve not lying on a quadric. If the generic plane section $\Gamma$ of $C$ is a complete intersection then $C$ is a complete intersection.
References
  • O. A. Laudal, A generalized trisecant lemma, Algebraic geometry (Proc. Sympos., Univ. Tromsø, Tromsø, 1977) Lecture Notes in Math., vol. 687, Springer, Berlin, 1978, pp. 112–149. MR 527232
  • Joe Harris, The genus of space curves, Math. Ann. 249 (1980), no. 3, 191–204. MR 579101, DOI 10.1007/BF01363895
  • R. Maggioni and A. Ragusa, The Hilbert function of generic plane sections of curves of $\textbf {P}^3$, Invent. Math. 91 (1988), no. 2, 253–258. MR 922800, DOI 10.1007/BF01389367
  • R. Strano, Sulle sezioni iperpiane delle curve, Rend. Sem. Mat. Fis. Milano (to appear).
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Additional Information
  • © Copyright 1988 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 104 (1988), 711-715
  • MSC: Primary 14M10; Secondary 14H50
  • DOI: https://doi.org/10.1090/S0002-9939-1988-0964847-X
  • MathSciNet review: 964847