We determine the singular locus of the holonomic system of differential equations annihilating Lauricella's hypergeometric function $F_C$ by the theory of $D$-modules and of Gröbner bases. We also study the $A$-hypergeometric system associated to $F_C$.
Ryohei HATTORI. Nobuki TAKAYAMA. "The singular locus of Lauricella's $F_C$." J. Math. Soc. Japan 66 (3) 981 - 995, July, 2014. https://doi.org/10.2969/jmsj/06630981