English

Double sections and dominating maps

Complex Variables 2016-09-07 v1

Abstract

As is well-known, given the complex sphere P^1 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 M\"obius 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 M\"obius transformation taking 1 to this puncture. In this paper we prove a parametrized version of this result.

Keywords

Cite

@article{arxiv.math/9904183,
  title  = {Double sections and dominating maps},
  author = {Gregery T. Buzzard and Steven Lu},
  journal= {arXiv preprint arXiv:math/9904183},
  year   = {2016}
}