Geodesic
On Fuchsian Systems with Given Asymptotics and Monodromy
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Algebra. Topology. Differential equations and their applications, Tome 224 (1999), pp. 112-121

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We discuss the problem of the existence of Fuchsian systems with given irreducible monodromies and given asymptotics of solutions at singular points, and construct a set of representations for which this problem has a negative solution. We also give an estimation of the codimension of this set in the moduli space of all irreducible representations. 
@article{TM_1999_224_a5,
     author = {A. A. Bolibrukh},
     title = {On {Fuchsian} {Systems} with {Given} {Asymptotics} and {Monodromy}},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {112--121},
     publisher = {mathdoc},
     volume = {224},
     year = {1999},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_1999_224_a5/}
}
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A. A. Bolibrukh. On Fuchsian Systems with Given Asymptotics and Monodromy. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Algebra. Topology. Differential equations and their applications, Tome 224 (1999), pp. 112-121. http://geodesic.mathdoc.fr/item/TM_1999_224_a5/