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.
The Theorem contradicts [CDP20, Cor. 2.3] as published.
- mr_mitm
100 pages of dense mathematics created by Claude. It doesn't even have an abstract or a summary. What are we looking at here? Has anyone read this? Please explain like I'm not a math PhD.
- scuppernong
- fjfaase
This kind of papers go way over my head, but recently I was surprised that ChatGTP (free) found the proof for an expression had a square value for some variables. It dug up a relationship from a paper from 2009 and correctly applied it to the case.
The chat: https://chatgpt.com/share/6a7f1b08-b9dc-83ea-b911-aaf8b65f1c...