Symplectic isotopy of rational cuspidal sextics and septics

Marco Golla (1, 2) , Fabien Kütle (2)

1 CNRS - Centre National de la Recherche Scientifique
2 LMJL - Laboratoire de Mathématiques Jean Leray

We classify rational cuspidal curves of degrees 6 and 7 in the complex projective plane, up to symplectic isotopy. The proof uses topological tools, pseudoholomorphic techniques, and birational transformations.

Domaines: Géométrie algébrique [math.AG]; Topologie géométrique [math.GT]; Géométrie symplectique [math.SG]

Marco Golla, Fabien Kütle. Symplectic isotopy of rational cuspidal sextics and septics. International Mathematics Research Notices, 2023, 2023 (8), pp.6504-6578. ⟨10.1093/imrn/rnab364⟩. ⟨hal-02929521⟩