  Let $d\geq3$ and $g\geq1$ be integers. Using a geometric construction
involving the symmetric product of a projective curve, we exhibit a
$d$-dimensional complete local normal domain over $\mathbb{C}$ with an isolated
singularity such that its class group contains a copy of
$(\mathbb{R}/\mathbb{Z})^{\oplus 2g}$ as subgroup.
