Monomial space curves in as binomial set theoretic complete intersections

Author:
Apostolos Thoma

Journal:
Proc. Amer. Math. Soc. **107** (1989), 55-61

MSC:
Primary 14M10

MathSciNet review:
976361

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We give a necessary and sufficient condition for monomial curves in 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.

**[H]**Robin Hartshorne,*Complete intersections in characteristic 𝑝>0*, Amer. J. Math.**101**(1979), no. 2, 380–383. MR**527998**, 10.2307/2373984**[M]**T. T. Moh,*Set-theoretic complete intersections*, Proc. Amer. Math. Soc.**94**(1985), no. 2, 217–220. MR**784166**, 10.1090/S0002-9939-1985-0784166-1**[R-V]**Lorenzo Robbiano and Giuseppe Valla,*Some curves in 𝑃³ are set-theoretic complete intersections*, Algebraic geometry—open problems (Ravello, 1982) Lecture Notes in Math., vol. 997, Springer, Berlin-New York, 1983, pp. 391–399. MR**714759****[Z-S]**Oscar Zariski and Pierre Samuel,*Commutative algebra. Vol. II*, The University Series in Higher Mathematics, D. Van Nostrand Co., Inc., Princeton, N. J.-Toronto-London-New York, 1960. MR**0120249**

Retrieve articles in *Proceedings of the American Mathematical Society*
with MSC:
14M10

Retrieve articles in all journals with MSC: 14M10

Additional Information

DOI:
http://dx.doi.org/10.1090/S0002-9939-1989-0976361-7

Keywords:
Monomial curves in projective -space,
binomial surfaces,
set theoretic complete intersections

Article copyright:
© Copyright 1989
American Mathematical Society