Real Algebraic and Analytic Geometry
Submission: 2003, November 5.
Given two nonsingular real algebraic varieties V and W, we consider the problem of deciding whether a smooth map f: V -> W can be approximated by regular maps in the space of smooth maps from V to W. Our main result is a complete solution to this problem in case W is the usual 2-dimensional sphere and V is a real algebraic surface of negative Kodaira dimension.
Mathematics Subject Classification (2000): 14P05 14P25 14J26.
Keywords and Phrases: ruled surfaces, conic bundle, approximation of smooth maps by regular maps.
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