Double sections and dominating maps
Gregery T. Buzzard, Steven Lu
Abstract
As is well-known, given the complex sphere P1 minus two points, there exist nonconstant holomorphic maps from the plane into this set, the simplest example of which is given by applying the exponential map and then composing with a Möbius transformation taking 0 and 1 to the two given punctures. Likewise, given the sphere minus one point, we can map the plane into this set by simply applying directly a Möbius transformation taking 1 to this puncture. In this paper we prove a parametrized version of this result.
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