Counterexamples to the complement problem

  • Pierre-Marie Poloni

    Universität Bern, Switzerland
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We provide explicit counterexamples to the so-called Complement Problem in every dimension , i.e. pairs of nonisomorphic irreducible algebraic hypersurfaces whose complements and 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, Counterexamples to the complement problem. Comment. Math. Helv. 94 (2019), no. 3, pp. 439–444

DOI 10.4171/CMH/464