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 is a set-theoretic complete intersection of two surfaces and with the multiplicity of along less than or equal to the multiplicity of along . One obtains a relation between the degrees of , and , the genus of , and the multiplicity of along in case has only ordinary singularities. One obtains (in the characteristic zero case) that a nonsingular rational curve of degree 4 in 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 .

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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