Combs and complex structures on the six-sphere

Jeff Viaclovsky

Source record

Source: arXiv

Published: Oct 7, 2026

arXiv: 2610.10451

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Source abstract

We construct complex structures on the six-sphere $S^6$ with arbitrarily large local Kuranishi dimension. As a corollary, we find the same phenomenon holds for the smooth manifold underlying complex projective 3-space $\mathbb{P}^3$ .

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Combs and complex structures on the six-sphere — Mathematical Frontier Network