  Archinard studied the curve $C$ over $\mathbb{C}$ associated to an
Appell-Lauricella hypergeometric series and differential forms on its
desingularization. In this paper, firstly as a generalization of Archinard's
results, we describe a partial desingularization of $C$ over a field $K$ under
a mild condition on its characteristic and the space of global sections of its
dualizing sheaf, especially we give an explicit basis of it. Secondly, when the
characteristic is positive, we show that the Cartier operator on the space can
be defined and describe it in terms of Appell-Lauricella hypergeometric series.
