Neighborhoods of rational curves without functions

Maycol Falla Luza (1) , Frank Loray (2)

1 UFF - Universidade Federal Fluminense [Rio de Janeiro]
2 IRMAR - Institut de Recherche Mathématique de Rennes

We prove the existence of (non compact) complex surfaces with a smooth rational curve embedded such that there does not exist any formal singular foliation along the curve. In particular, at arbitray small neighborhood of the curve, any meromorphic function is constant. This implies that the Picard group is not countably generated.

Domaines: Variables complexes [math.CV]; Géométrie algébrique [math.AG]

Maycol Falla Luza, Frank Loray. Neighborhoods of rational curves without functions. Mathematische Annalen, 2022, 382, pp.1047-1058. ⟨10.1007/s00208-020-02126-x⟩. ⟨hal-02526096v2⟩