Conférencier : Xi Chen, Université de l'Alberta

Résumé : A cusp is a curve singularity that is locally irreducible. A cuspidal curve is a curve with only cusps as singularities. Topologically, a cuspidal curve is homeomorphic to its normalization. Rational cuspidal curves on the projective plane have been extensively studied classically. Rational curves with one, two and three cusps were explicitly constructed. It is known that the number of cusps of these curves are bounded, regardless of the degree of the curve. It is conjectured that there are no rational cuspidal plane curves with 5 or more cusps. On the other hand, the degrees of these curves are unbounded. We will study rational cuspidal curves on K3 surfaces. On K3 surfaces, there is actually an upper bound for the degree of these curves. This is a joint work with Frank Gounelas.