Conditional complex structure on $S^{2}\times S^{4}$ reported

Lineage and corrections

This event attributed to VibeMathed

Assuming the cited compact complex threefold $X_{\mathrm{sph}}$ on the smooth $S^{6}$ is valid, blowing up its fixed curve, quotienting by the order-two action, and applying an Atiyah flop produces a complex threefold $X_{+}$ diffeomorphic to the standard smooth manifold $S^{2}\times S^{4}$. parent of this event

This event evidence for Assuming the cited compact complex threefold $X_{\mathrm{sph}}$ on the smooth $S^{6}$ is valid, blowing up its fixed curve, quotienting by the order-two action, and applying an Atiyah flop produces a complex threefold $X_{+}$ diffeomorphic to the standard smooth manifold $S^{2}\times S^{4}$.

Liang, Liu, and Zhang, arXiv:2608.29651v1 evidence for this event

This event attributed to Ruiming Liang

VibeMathed record for a complex structure on $S^{2}\times S^{4}$ evidence for this event

This event attributed to Chenhan Liu

This event attributed to Yang Zhang

This event derived from Remarks on the Complex Structures on $\mathbb{P}^{3}$ and $S^{2}\times S^{4}$

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

A complex structure on $S^{2}\times S^{4}$ parent of this event