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

  • Toshio Oshima

    Josai University, Tokyo, Japan
Versal Unfolding of Irregular Singularities of a Linear Differential Equation on the Riemann Sphere cover
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Abstract

For a linear differential operator PP on P1\mathbb{P}^1 with unramified irregular singular points, we examine a realization of PP as a confluence of singularities of a Fuchsian differential operator P~\widetilde{P} having the same index of rigidity as PP, which we call an unfolding of PP. We conjecture that this is always possible. For example, if PP is rigid, this is true and the unfolding helps us to study the equation Pu=0Pu=0.

Cite this article

Toshio Oshima, Versal Unfolding of Irregular Singularities of a Linear Differential Equation on the Riemann Sphere. Publ. Res. Inst. Math. Sci. 57 (2021), no. 3/4, pp. 893–920

DOI 10.4171/PRIMS/57-3-6