  An \emph{$\mathbb{R}$-join-type curve} is a curve in $\mathbb{C}^2$ defined
by an equation of the form \begin{equation*} a\cdot\prod_{j=1}^\ell
(y-\beta_j)^{\nu_j} = b\cdot\prod_{i=1}^m (x-\alpha_i)^{\lambda_i},
\end{equation*} where the coefficients $a$, $b$, $\alpha_i$ and $\beta_j$ are
\emph{real} numbers. For generic values of $a$ and $b$, the singular locus of
the curve consists of the points $(\alpha_i,\beta_j)$ with $\lambda_i,\nu_j\geq
2$ (so-called \emph{inner} singularities). In the non-generic case, the inner
singularities are not the only ones: the curve may also have \emph{`outer'}
singularities. The fundamental groups of (the complements of) curves having
only inner singularities are considered in \cite{O}. In the present paper, we
investigate the fundamental groups of a special class of curves possessing
outer singularities.

Algebraic Geometry