Dima Arinkin, University of North Carolina at Chapel Hill

Rigid differential equations

We study systems of linear ordinary differential equations dy/dz=A(z)y, where A is a matrix-valued rational function of z. By definition, such equation is rigid if it is uniquely determined by the type of its singularities.

Our goal is to provide a classification of rigid equations. If all singularities of A are regular, this was done by N.Katz; we extend his results to arbitrary A.

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