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New distinct curves having the same complement in the projective plane

Costa, Paolo

In: Mathematische Zeitschrift, 2012, vol. 271, no. 3-4, p. 1185-1191

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    Titre
    • New distinct curves having the same complement in the projective plane
    Auteur
    • Costa, Paolo. UniGe, Genève, Suisse
    Type de document
    • Postprint
    Langue
    • Inglese
    Publié dans
    • Mathematische Zeitschrift, 2012, vol. 271, no. 3-4, p. 1185-1191. Springer-Verlag
    Autre version électronique
    Classification
    • Mathématiques
    Identifiant OAI-PMH
    • oai:doc.rero.ch:320969
    Summary
    In 1984, Yoshihara conjectured that if two plane irreducible curves have isomorphic complements, they are projectively equivalent, and proved the conjecture for a special family of unicuspidal curves. Recently, Blanc gave counterexamples of degree 39 to this conjecture, but none of these is unicuspidal. In this text, we give a new family of counterexamples to the conjecture, all of them being unicuspidal, of degree 4m+1 for any m≥2. In particular, we have counterexamples of degree 9, which seems to be the lowest possible degree