Fibrations on the 6-sphere and Clemens threefolds

Nobuhiro Honda; Jeff Viaclovsky

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arXiv · 2403.05035

Fibrations on the 6-sphere and Clemens threefolds

Nobuhiro Honda·Jeff Viaclovsky

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Abstract

Let $Z$ be a compact, connected $3$-dimensional complex manifold with vanishing first and second Betti numbers and non-vanishing Euler characteristic. We prove that there is no surjective holomorphic mapping from $Z$ onto any $2$-dimensional complex space. In other words, $Z$ can only possibly fiber over a curve. This result applies in particular to a class of threefolds, known as Clemens threefolds, which are diffeomorphic to a connected sum $k \# (S^3 \times S^3)$ for $k \geq 2$. This result also gives a new restriction on any hypothetical complex structure on the $6$-sphere $S^6$.

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BibTeX RIS

Nobuhiro Honda, Jeff Viaclovsky. 2024-03-08. Fibrations on the 6-sphere and Clemens threefolds. https://arxiv.org/abs/2403.05035

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