Additive Deligne-Simpson Problem for Non-Fuchsian Systems

概要

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We consider the problem for which tuples of conjugacy classes cj ⊂ gl (n, C) and for which tuples of non-resonant formal normal forms does there exist a non-Fuchsian linear system of ordinary differential equations on Riemanns sphere with residue matrices from the classes cj and with the given formal normal forms at its poles. It turns out that the answer is the same as in the case of Fuchsian systems and depends only on the conjugacy classes cj. We find also the dimension of the moduli space of such non-Fuchsian systems.