Groebner basis and singular locus of Lauricella's hypergeometric differential equations

We derive Groebner bases for Lauricella’s hypergeometric differential equations $I_A(m),I_B(m),I_C(m)$ with respect to a monomial order. By using these Groebner bases, we determine characteristic varieties and the singular loci of $I_A(m),I_B(m),I_C(m)$.