Pfaffian systems of Fuchs type on a complex analytic manifold

In this paper we give necessary and sufficient conditions for a completely integrable Pfaffian system with regular singular points on $A$ to be a Fuchsian system, where $A$ is a divisor with normal crossings in a compact Kähler manifold $W^m$. We prove that the condition of being a Fuchsian system is equivalent to the solvability of some first Cousin problem on $W^m$. This condition appears particularly simple when $W^m$ is complex projective space.
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