Additive Deligne-Simpson Problem for Non-Fuchsian Systems

MR2761090 Vladimir P. KOSTOV Vladimir P. KOSTOV Additive Deligne-Simpson Problem for Non-Fuchsian Systems Funkcialaj Ekvacioj. Serio Internacia 53 2010 395--410 http://fe.math.kobe-u.ac.jp/FE/FullPapers/53-3/53_395.pdf http://www.ams.org/mathscinet-getitem?mr=MR2761090 We consider the problem for which tuples of conjugacy classes $c_j\subset gl(n,\mathbb{C})$ and for which tuples of non-resonant formal normal forms does there exist a non-Fuchsian linear system of ordinary differential equations on Riemann's sphere with residue matrices from the classes $c_j$ and with the given formal normal forms. It turns out that the answer is the same as in the case of Fuchsian systems and depends only on the conjugacy classes $c_j$. We find also the dimension of the moduli space of such non-Fuchsian systems. (Non-)Fuchsian system, Monodromy, Deligne-Simpson problem, Moduli space. Primary 15A24; 34M50; Secondary 34M35. 53-395 2010 Additive Deligne-Simpson Problem for Non-Fuchsian Systems Vladimir P. KOSTOV Vladimir P. KOSTOV 1 Balser, W.; Jurkat, W. B.; Lutz, D. A. A general theory of invariants for meromorphic differential equations. I, Formal invariants Funkcial. Ekvac. 22 1979 197-221 MR0556577 0556577 2 Balser, W.; Jurkat, W. B.; Lutz, D. A. A general theory of invariants for meromorphic differential equations. II, Proper invariants Funkcial. Ekvac. 22 1979 257-283 MR0577846 0577846

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