Rational surfaces and regular maps into the 2-dimensional sphere |
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Authors: | Nuria Joglar-Prieto |
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Institution: | (1) Department of Mathematics and Statistics, University of New Mexico, Albuquerque, NM, 87131, USA, US |
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Abstract: | Let X and Y be affine nonsingular real algebraic varieties. A general problem in Real Algebraic Geometry is to try to decide when a mapping, , can be approximated by regular mappings in the space of mappings, , equipped with the topology. In this paper, we obtain some results concerning this problem when the target space is the 2-dimensional standard
sphere and X has a complexification that is a rational (complex) surface. To get the results we study the subgroup of the second cohomology group of X with integer coefficients that consists of the cohomology classes that are pullbacks, via the inclusion mapping , of the cohomology classes in represented by complex algebraic hypersurfaces.
Received December 1, 1998; in final form August 2, 1999 |
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