On the fundamental groups of non-generic ℝ-join-type curves, II

Abstract

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 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 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.