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Licensed Unlicensed Requires Authentication Published by De Gruyter June 16, 2009

The correspondence between a plane curve and its complement

  • Jérémy Blanc


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.

Received: 2008-02-19
Published Online: 2009-06-16
Published in Print: 2009-August

© Walter de Gruyter Berlin · New York 2009

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