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

Year: 2026

Type: preprint

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 $S^{2}\times S^{4}$.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2608.29651

Authors: Liang, Ruiming, Liu, Chenhan, Zhang, Yang

Topic: Geometry and complex manifolds

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W7204890313

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