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arXiv · 1605.05169

Counterexamples to the Complement Problem

Pierre-Marie Poloni
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Abstract

We provide explicit counterexamples to the so-called Complement Problem in every dimension $n\geq3$, i.e. pairs of non-isomorphic irreducible hypersurfaces $H_1, H_2\subset\mathbb{C}^{n}$ whose complements $\mathbb{C}^{n}\setminus H_1$ and $\mathbb{C}^{n}\setminus H_2$ are isomorphic. Since we can arrange that one of the hypersurfaces is singular whereas the other is smooth, we also have counterexamples in the analytic setting.

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Pierre-Marie Poloni. 2017-02-10. Counterexamples to the Complement Problem. https://arxiv.org/abs/1605.05169

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