The complex geometry of a hypothetical complex structure on S6

This article is a survey about or introduction to certain aspects of the complex geometry of a hypothetical complex structure on the six-sphere. We discuss a result of Peternell-Campana-Demailly on the algebraic dimension of a hypothetical complex six-sphere and give some examples. We also give an overview over an application of Huckleberry-Kebekus-Peternell on the group of biholomorphisms of such a complex six-sphere.