Algebraic models defined over Q of differential manifolds
Article
Received:
Revised:
- 28 Downloads
- 2 Citations
Abstract
Here we prove that every compact differential manifold has a smooth algebraic model defined over Q. In dimension 2 we find an algebraic model (may be singular) defined over Q and birational over Q to the projective plane.
1980 Mathematics Subject Classifications (1985 Revision)
Primary 14G30 Secondary 57R12, 55N22, 14G05Preview
Unable to display preview. Download preview PDF.
References
- 1.Grothendieck, A. and Dieudonné, J., ‘Eléments de Géometrie Algébrique: EGA IV. Etude locale des schémas et des morphismes de schémas’, Publ. Math. IHES 20 (1964), 24 (1965), 28 (1966), 32 (1967).Google Scholar
- 2.Hartshorne, R., Algebraic Geometry, GTM 52, Springer-Verlag, Berlin, 1977.Google Scholar
- 3.Milnor, J., ‘On the Stiefel Whitney numbers of complex manifolds and spin manifolds’, Topology 3 (1965), 223–230.Google Scholar
- 4.Tognoli, A., ‘Algebraic approximation of manifolds and spaces’, Sem. Bourbaki 1979–80, exp. no. 548, Lecture Notes in Math. 842, Springer-Verlag, Berlin, 1981.Google Scholar
- 5.Tognoli, A., ‘Algebraic functions and Nash functions’, Institutiones Mathematicae, Vol. 3, Academic Press, London and New York, 1978.Google Scholar
- 6.Whitney, H., ‘Differentiable manifolds’, Ann. Math. 37 (1936), 647–680.Google Scholar
Copyright information
© Kluwer Academic Publishers 1992