The Hypergeometric Differential Equation 3e2 with Cubic Curves as Schwarz Images

Let 3E2(a1, a2, a3; b1, b2) denote the generalized hypergeometric differential equation of rank three with parameters (a1, a2, a3, b1, b2), which is defined on the projective line P(x) with reuglar singularities at x = 0, 1,∞. Any set of linearly independent solutions defines a multi-valued map from P − {0, 1,∞} to the projective plane P called the Schwarz map. The image of this map is locally a curve, determined uniquely up to projective transformations. The condition for the image curve to be a cubic curve is written in terms of the parameters, and we list up those curves and study the action of the monodromy groups on these curves.