Geodesic
On the local fundamental group of the complement of a~curve in a~normal surface
Izvestiya. Mathematics , Tome 87 (2023) no. 3, pp. 562-585

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We give a presentation of the fundamental group of the complement of a curve $C$ in its “tubular” neighbourhood in a normal surface $S$. The presentation is given in terms of the double weighted dual graph of the resolution of singularities of $C$ (and $S$). This result generalizes the presentation of the fundamental group of the complement of a normal singularity in its neighbourhood given by Mumford in the case, where the dual graph of the resolution is a tree and all exceptional curves of the resolution are rational curves.
Keywords: tubular neighbourhood of complex curve, fundamental group. 
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     title = {On the local fundamental group of the complement of a~curve in a~normal surface},
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Vik. S. Kulikov. On the local fundamental group of the complement of a~curve in a~normal surface. Izvestiya. Mathematics , Tome 87 (2023) no. 3, pp. 562-585. http://geodesic.mathdoc.fr/item/IM2_2023_87_3_a5/