Speaker: Jérémy Blanc (Basel)

Title: On complements of curves in the projective plane

Abstract: The complement of an irreducible curve in the projective space is an affine surface. Are there different curves which have the same complement? In 1984, H. Yoshihara conjectured that no such example existed. I will present the cases where the conjecture is true, and show a special counterexample, of degree 39. Then, I will explain a recent construction which provide a family of unicuspidal curves providing counterexamples, and having degree 9, 13,17,...