The correspondence between a plane curve and its complement

Blanc, Jérémy. (2009) The correspondence between a plane curve and its complement. Journal für die reine und angewandte Mathematik, Bd. 633. pp. 1-10.

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Official URL: http://edoc.unibas.ch/dok/A5842751

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Given two irreducible curves of the plane which have isomorphic complements, it is natural to ask whether there exists an automorphism of the plane that sends one curve on the other. This question has a positive answer for a large family of curves and H. Yoshihara conjectured that it is true in general. We exhibit counterexamples to this conjecture, over any ground field. In some of the cases, the curves are isomorphic and in others not; this provides counterexamples of two different kinds. Finally, we use our construction to find the existence of surprising non-linear automorphisms of affine surfaces.
Faculties and Departments:05 Faculty of Science > Departement Mathematik und Informatik > Mathematik > Algebra (Blanc)
UniBasel Contributors:Blanc, Jérémy
Item Type:Article, refereed
Article Subtype:Research Article
Publisher:Walter de Gruyter
Note:Publication type according to Uni Basel Research Database: Journal article
Identification Number:
Last Modified:08 Jun 2012 06:56
Deposited On:08 Jun 2012 06:48

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