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arXiv · 2608.29651

Remarks on the Complex Structures on $\mathbb P^3$ and $S^2\times S^4$

Ruiming Liang·Chenhan Liu·Yang Zhang
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Abstract

Assuming the validity of the recently proposed \textit{``A compact complex threefold fibred by tori over the projective line, and the six-sphere''}, we construct an exotic complex structure on $\mathbb P^{3}$, distinct from the point-blowup structures of Huckleberry, Kebekus, and Peternell. Then we perform an Atiyah flop to produce a complex structure on the standard smooth manifold $S^{2}\times S^{4}$.

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Ruiming Liang, Chenhan Liu, Yang Zhang. 2026-08-30. Remarks on the Complex Structures on $\mathbb P^3$ and $S^2\times S^4$. https://arxiv.org/abs/2608.29651

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