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arXiv · 1011.6337

New distinct curves having the same complement in the projective plane

Paolo Costa
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Abstract

In 1984, H. 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, J. 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 \geq 2. In particular, we have counterexamples of degree 9, which seems to be the lowest possible degree.

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Paolo Costa. 2010-11-29. New distinct curves having the same complement in the projective plane. https://arxiv.org/abs/1011.6337

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