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arXiv · 2410.07207

Compactifications of C^n and the complex projective space

Thomas Peternell
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Abstract

We show that the complex projective space is the only projective manifold compactifying $\mathbb{C}^n$ by a smooth connected hypersurface, provided $n$ is even. In the odd dimensional case we give some partial results. The case when $n \equiv 1 $ mod $4$ has now been settled by Ping Li.

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Thomas Peternell. 2024-09-25. Compactifications of C^n and the complex projective space. https://arxiv.org/abs/2410.07207

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