The $(3,4,\infty)$ Modular Family of 2-Tori as a Complex Structure on $S^6$

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This event attributed to Levent Alpöge

This event attributed to Claude

Campana, Demailly, Peternell - the corrigendum this paper contradicts evidence for this event

Hacker News discussion evidence for this event

Explanation by Philip Engel evidence for this event

VibeMathed record: The $(3,4,\infty)$ Modular Family of 2-Tori as a Complex Structure on $S^6$ evidence for this event

The $(3,4,\infty)$ Modular Family of 2-Tori as a Complex Structure on $S^6$ parent of this event

The $(3,4,\infty)$ Modular Family of 2-Tori as a Complex Structure on $S^6$ evidence for this event

Formalization by Boris Alexeev evidence for this event

Claims an explicit compact complex threefold $X$, fibred over $\mathbb{P}^1$ by complex 2-tori via period functions on the $(3,4,\infty)$ orbifold, degenerating to a del Pezzo-of-degree-six fibre (identified opposite sides of its hexagon) at one point and to bielliptic multiple fibres of multiplicities 3 and 4 at the other two. Argues $X$ is simply connected with $H_*(X;\mathbb{Z})=H_*(S^6;\mathbb{Z})$, hence diffeomorphic to $S^6$, with algebraic dimension exactly 1. This directly contradicts [CDP20, Cor. 2.3], a published (and once-corrected) theorem; the paper states this and argues where the two accounts diverge, rather than overlooking it. Posted hours before this entry, with no independent check, no formalisation, and no refutation yet in any venue found. Filed as a candidate specifically because none of that has happened, not because a problem with the argument has been found. parent of this event

Alpöge's announcement, quoted in full, via Digg's coverage evidence for this event

Agricola, Bazzoni, Goertsches, Konstantis, Rollenske - On the history of the Hopf problem evidence for this event