Le probléme de Riemann-Hilbert sur une variété analytique complexe (Q2533432)

The Riemann-Hilbert problem for a complex manifold \(V\) is the following: Let \(A\) be an analytic subset of \(V\) of codimension one at each of its points and \(\chi \) be a representation of \(\Pi_1(V-A)\) into the linear group \(\mathrm{GL}(n,\mathbb C)\). Does there exists a Pfaffian system of Fuchs type whose monodromy is the class of the representation \(\chi \)? It is proved that if \(V\) is a contractible Stein manifold and if the irreducible components of \(A\) are without singularities and in general position then the Riemann-Hilbert problem admits a solution.