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Non-homotopicity of the linking set of algebraic plane curves

Benoît Guerville-Ballé

Department of Mathematics, Tokyo Gakugei University, Koganei-shi, Tokyo 184-8501, Japan

E-mail Address: benoit.guerville-balle@math.cnrs.fr

www.benoit-guervilleballe.com

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and

Taketo Shirane

National Institute of Technology, Ube College, 2-14-1 Tokiwadai, Ube 755-8555, Yamaguchi, Japan

E-mail Address: tshirane@ube-k.ac.jp

Corresponding author.

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https://doi.org/10.1142/S0218216517500894Cited by:5 (Source: Crossref)

Abstract

The linking set is an invariant of algebraic plane curves introduced by Meilhan and the first author. It has been successfully used to detect several examples of Zariski pairs, i.e. curves with the same combinatorics and different embedding in $ℂ ℙ^{2}$ . Differentiating Shimada's $π_{1}$ -equivalent Zariski pair by the linking set, we prove, in the present paper, that this invariant is not determined by the fundamental group of the curve.

Keywords:

AMSC: 14H50, 14H30, 14F45

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