New distinct curves having the same complement in the projective plane

Article Article scientifique Article New distinct curves having the same complement in the projective plane eng 2012 author Costa Paolo 632177 1185-1191 10.1007/s00209-011-0909-4 0025-5874 http://link.springer.com/10.1007/s00209-011-0909-4 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. Dewey 510 Open Access - Licence nationale Springer 25 Section de mathématiques 11 false Mathematische Zeitschrift 271 3-4 800ef62d-5695-4f68-b250-753fa6478c1e Article (Published version) Public Costa2012_Article_NewDistinctCurvesHavingTheSame.pdf 202554 application/pdf openAccess Faculté des sciences / Section de mathématiques

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New distinct curves having the same complement in the projective plane	Mathematische Zeitschrift			2012	388	208

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Costa, Paolo