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On Complete Intersections Over an Algebraically Non-Closed Field

Published online by Cambridge University Press:  20 November 2018

Maria Grazia Marinari  and
Mario Raimondo
Maria Grazia Marinari
Affiliation:
Istituto Di Matematica Universita di Genova, 16132, Genova, Italy
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Abstract

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We give a criterion in order that an affine variety defined over any field has a complete intersection (ci.) embedding into some affine space. Moreover we give an example of a smooth real curve C all of whose embeddings into affine spaces are c.i.; nevertheless it has an embedding into ℝ3 which cannot be realized as a c.i. by polynomials.

Keywords

14M1014G30
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 29 , Issue 2 , 01 June 1986 , pp. 140 - 145
Copyright
Copyright © Canadian Mathematical Society 1986

References

1. Altman, A., Kleiman, S., Introduction to Grothendieck Duality Theory, Lect. Notes in Math. 146, Springer Verlag, 1970.Google Scholar
2. Bochnak, J., Kucharz, W., On complete intersections in differential topology and analytic geometry, Preprint 1982.Google Scholar
3. Gross, B., Harris, J., Real algebraic curves, Ann. Scient. Ec. Norm. Sup. 4e 14, 1981.Google Scholar
4. Marinari, M.G., Odetti, F., and Raimondo, M., Affine curves over an algebraically non-closed field, Pac. J. Math. 107, 1983.Google Scholar
5. Marinari, M.G. and Raimondo, M., Properties of the regular functions ring of affine varieties defined over any field, Rend. Sem. Mat. Univ. e Pol. Torino, 37, 1979.Google Scholar
6. Mohan Kumar, N., Complete intersections, J. Math. Kyoto Univ. 17-3, 1977.Google Scholar
7. Pavaman Murthy, N., Generators for certain ideals in regular rings of dimension three; Comment. Math. Helv. 47, 1972.Google Scholar
8. Renschuch, B., Betràge zur konstruktiven Théorie der Polynomideale. XVIII, Padagog. Hoch. K. Liebknecht Potsdam, 27, 1983.Google Scholar
9. Tognoli, A., Algebraic Geometry and Nash functions, INDAM 3, 1978.Google Scholar