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arXiv · 1906.10626

On compactifications of affine homology 3-cells into quadric fibrations

Masaru Nagaoka
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Abstract

In this paper we deal with compactifications of affine homology $3$-cells into quadric fibrations such that the boundary divisors contain fibers. We show that all such affine homology $3$-cells are isomorphic to the affine $3$-space $\mathbb{A}^{3}$. Moreover, we show that all such compactifications can be connected by explicit elementary links preserving $\mathbb{A}^{3}$ to the projective $3$-space $\mathbb{P}^{3}$.

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Masaru Nagaoka. 2019-06-25. On compactifications of affine homology 3-cells into quadric fibrations. https://arxiv.org/abs/1906.10626

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