On the local fundamental group of the complement to a curve in a normal surface
- Authors: Kulikov V.S.1
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Affiliations:
- Steklov Mathematical Institute of Russian Academy of Sciences
- Issue: Vol 87, No 3 (2023)
- Pages: 149-174
- Section: Articles
- URL: https://journals.rcsi.science/1607-0046/article/view/133917
- DOI: https://doi.org/10.4213/im9357
- ID: 133917
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Abstract
In the article, we give a presentation of the fundamental group of the complement to a curve $C$ in its "tubular" neighborhood in a normal surface $S$. The presentation is given in terms of the double weighted dual graph of a resolution of singularities of $C$ (and $S$)and it is a generalization of the presentation of the fundamental group of the complement to a normal singularity in its neighborhood given by Mumford in the case when the dual graph of resolution is a tree and all exceptional curves of the resolution are rational curves.
About the authors
Victor Stepanovich Kulikov
Steklov Mathematical Institute of Russian Academy of Sciences
Email: kulikov@mi-ras.ru
Doctor of physico-mathematical sciences, Professor
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