Abstract
In this paper we give necessary and sufficient conditions for a completely integrable Pfaffian system with regular singular points on to be a Fuchsian system, where is a divisor with normal crossings in a compact Kahler manifold . We prove that the condition of being a Fuchsian system is equivalent to the solvability of some first Cousin problem on . This condition appears particularly simple when is complex projective space.Bibliography: 12 titles.
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