A complex structure on S^6

A complex structure on S^6 [pdf]

This paper constructs a compact complex 3-manifold X that is diffeomorphic to the 6-sphere S^6, providing a complex structure on S^6. The construction uses a family of complex 2-tori over a punctured orbifold curve, completed at three special points via logarithmic transforms and a toric degeneration. The resulting threefold has the integral homology of S^6, is simply connected, and has algebraic dimension 1. The paper also explains why a previous argument against such a structure does not apply.