Versal Unfolding of Irregular Singularities of a Linear Differential Equation on the Riemann Sphere

Abstract

For a linear differential operator P on P1 with unramified irregular singular points we examine a realization of P as a confluence of singularities of a Fuchsian differential operator P̃ having the same index of rigidity as P , which we call an unfolding of P . We conjecture that this is always possible. For example, if P is rigid, this is true and the unfolding helps us to study the equation Pu = 0.