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Journal Articles Mathematische Annalen Year : 2022

Neighborhoods of rational curves without functions

Abstract

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.
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Dates and versions

hal-02526096 , version 1 (31-03-2020)
hal-02526096 , version 2 (01-04-2020)

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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⟩
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