法曲面上曲线补的局部基群

IF 0.8 3区数学 Q2 MATHEMATICS

Izvestiya Mathematics Pub Date : 2023-01-01 DOI:10.4213/im9357e

Victor Stepanovich Kulikov

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引用次数: 0

摘要

给出了法曲面S$上曲线C$在其管状邻域中补的基本群。给出了$C$(和$S$)奇异点解析的双加权对偶图。在分辨率的对偶图为树且分辨率的所有异常曲线为有理曲线的情况下，推广了Mumford给出的邻域正常奇点补的基本群的表示。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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On the local fundamental group of the complement of a curve in a normal surface

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.

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来源期刊

Izvestiya Mathematics 数学-数学

CiteScore

1.30

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： The Russian original is rigorously refereed in Russia and the translations are carefully scrutinised and edited by the London Mathematical Society. This publication covers all fields of mathematics, but special attention is given to: Algebra; Mathematical logic; Number theory; Mathematical analysis; Geometry; Topology; Differential equations.