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

Monomial space curves in $ {\bf P}\sp 3\sb k$ as binomial set theoretic complete intersections


Author: Apostolos Thoma
Journal: Proc. Amer. Math. Soc. 107 (1989), 55-61
MSC: Primary 14M10
MathSciNet review: 976361
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Abstract: We give a necessary and sufficient condition for monomial curves in $ P_k^3$ to be set theoretic complete intersections on a binomial surface. Using this condition, we prove that the twisted cubic curve is the only smooth monomial curve which is a set theoretic complete intersection on a binomial surface, in characteristic zero.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1989-0976361-7
PII: S 0002-9939(1989)0976361-7
Keywords: Monomial curves in projective $ 3$-space, binomial surfaces, set theoretic complete intersections
Article copyright: © Copyright 1989 American Mathematical Society