The complex geometry of a hypothetical complex structure on $S^6$

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.

References in corpus (3)

• Almost complex structures on spheres
• The algebraic dimension of compact complex threefolds with vanishing second Betti numbers
• Hodge numbers of a hypothetical complex structure on $S^6$

Cited by in corpus (2)

• The algebraic dimension of compact complex threefolds with vanishing second Betti numbers
• On the history of the Hopf problem