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New distinct curves having the same complement in the projective plane

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Published in Mathematische Zeitschrift. 2012, vol. 271, no. 3-4, p. 1185-1191
Collection Open Access - Licence nationale Springer 
Abstract 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.
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COSTA, Paolo. New distinct curves having the same complement in the projective plane. In: Mathematische Zeitschrift, 2012, vol. 271, n° 3-4, p. 1185-1191. doi: 10.1007/s00209-011-0909-4 https://archive-ouverte.unige.ch/unige:111997

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Deposited on : 2018-12-05

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