Abstract
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.
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