Neighborhoods of rational curves without functions

2020/03/29 by Luza, Maycol Falla, Loray, Frank · 1 citation
#Algebraic Geometry (math.AG) #Classical Analysis and ODEs (math.CA) #Complex Variables (math.CV) #FOS: Mathematics

paper · doi:10.48550/arxiv.2003.14212

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.

Cited by

• Neighborhoods of curves with a prescribed number of foliations

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