New distinct curves having the same complement in the projective plane
Algebraic Geometry
2010-11-30 v1
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.
Keywords
Cite
@article{arxiv.1011.6337,
title = {New distinct curves having the same complement in the projective plane},
author = {Paolo Costa},
journal= {arXiv preprint arXiv:1011.6337},
year = {2010}
}