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Proceedings of the American Mathematical Society

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

 

 

On the curves of contact on surfaces
in a projective space. III


Author: M. Boratynski
Journal: Proc. Amer. Math. Soc. 125 (1997), 329-338
MSC (1991): Primary 14H50
DOI: https://doi.org/10.1090/S0002-9939-97-03532-6
MathSciNet review: 1346964
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Abstract: Suppose a smooth curve $C$ is a set-theoretic complete intersection of two surfaces $F$ and $G$ with the multiplicity of $F$ along $C$ less than or equal to the multiplicity of $G$ along $C$. One obtains a relation between the degrees of $C$, $F$ and $G$, the genus of $C$, and the multiplicity of $F$ along $C$ in case $F$ has only ordinary singularities. One obtains (in the characteristic zero case) that a nonsingular rational curve of degree 4 in $\mathbf P^3 $ is not set-theoretically an intersection of 2 surfaces, provided one of them has at most ordinary singularities. The same result holds for a general nonsingular rational curve of degree $\geq 5$.


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Additional Information

M. Boratynski
Affiliation: Dipartimento di Matematica, via E Orabona 4, 70125 Bari, Italy
Email: boratyn@pascal.dm.uniba.it

DOI: https://doi.org/10.1090/S0002-9939-97-03532-6
Received by editor(s): July 25, 1994
Received by editor(s) in revised form: December 13, 1994, and June 27, 1995
Additional Notes: This research was supported by the funds of the Italian Ministry of Education and Scientific Research (MURST)
Communicated by: Wolmer V. Vasconcelos
Article copyright: © Copyright 1997 American Mathematical Society