Open Access
January, 2017 On the fundamental groups of non-generic $\mathbb{R}$-join-type curves, II
Christophe EYRAL, Mutsuo OKA
J. Math. Soc. Japan 69(1): 241-262 (January, 2017). DOI: 10.2969/jmsj/06910241


We study the fundamental groups of (the complements of) plane complex curves defined by equations of the form $f(y)=g(x)$, where $f$ and $g$ are polynomials with real coefficients and real roots (so-called $\mathbb{R}$-join-type curves). For generic (respectively, semi-generic) such polynomials, the groups in question are already considered in [6] (respectively, in [3]). In the present paper, we compute the fundamental groups of $\mathbb{R}$-join-type curves under a simple arithmetic condition on the multiplicities of the roots of $f$ and $g$ without assuming any (semi-)genericity condition.


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Christophe EYRAL. Mutsuo OKA. "On the fundamental groups of non-generic $\mathbb{R}$-join-type curves, II." J. Math. Soc. Japan 69 (1) 241 - 262, January, 2017.


Published: January, 2017
First available in Project Euclid: 18 January 2017

zbMATH: 1368.14041
MathSciNet: MR3597554
Digital Object Identifier: 10.2969/jmsj/06910241

Primary: 14H30
Secondary: 14H20 , 14H45 , 14H50

Keywords: bifurcation graph , fundamental group , Monodromy , plane curves , Zariski–van Kampen's pencil method

Rights: Copyright © 2017 Mathematical Society of Japan

Vol.69 • No. 1 • January, 2017
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