Marius van der Put

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The methods of [vdP-Sa, vdP1, vdP2] are applied to the fourth Painlevé equation. One obtains a Riemann– Hilbert correspondence between moduli spaces of rank two connections on P1 and moduli spaces for the monodromy data. The moduli spaces for these connections are identified with Okamoto–Painlevé varieties and the Painlevé property follows. For an explicit(More)
The classical solution of the Riemann]Hilbert problem attaches to a given representation of the fundamental group a regular singular linear differential equation. We present a method to compute this differential equation in the case of a representation with finite image. The approach uses Galois coverings of P1 _ 4 0, 1, ` , differential Galois theory, and(More)
a r t i c l e i n f o a b s t r a c t The notion of strict equivalence for order one differential equations of the form f (y , y, z) = 0 with coefficients in a finite extension K of C(z) is introduced. The equation gives rise to a curve X over K and a derivation D on its function field K (X). Procedures are described for testing strict equivalence, strict(More)