On the recovery of a~Pfaffian system of Fuchsian type from the generators of the monodromy group
Izvestiya. Mathematics , Tome 17 (1981) no. 2, pp. 227-241.

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From relations of the fundamental group $\pi_1(C^n-L)$ the author obtains commutation relations for the coefficient matrices of a Pfaffian system of Fuchsian type in $C^n$, with manifold of singularities on the union of a finite number of hyperplanes $L$. Expansions of the coefficient matrices in powers of the logarithms of the generators of the monodromy group are given under the condition that these matrices are close to the identity. Bibliography: 30 titles.
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V. A. Golubeva. On the recovery of a~Pfaffian system of Fuchsian type from the generators of the monodromy group. Izvestiya. Mathematics , Tome 17 (1981) no. 2, pp. 227-241. http://geodesic.mathdoc.fr/item/IM2_1981_17_2_a0/

[1] Gérard R., “Théorie de Fuchs sur une variété analytique complexe”, J. math. pure et appl., 47:4 (1968), 321–404 | MR | Zbl

[2] Zariski O., Algebraic surfaces, Springer, N. Y., 1971 | MR | Zbl

[3] Kampen E. van, “On the connection between the fundamental groups of some connected spaces”, Am. J. Math., 55:2 (1933), 261–267 | Zbl

[4] Bolibrukh A. A., “O fundamentalnoi matritse sistemy Pfaffa tipa Fuksa”, Izv. AN SSSR. Ser. matem., 41 (1977), 1084–1109 | Zbl

[5] Bolibrukh A. A., “Sistemy Pfaffa tipa Fuksa na kompleksnom analiticheskom mnogoobrazii”, Matem. sb., 103(145):1(5) (1977), 112–123 | MR | Zbl

[6] Golubeva V. A., “O meromorfnom sechenii kompleksno-analiticheskogo vektornogo rassloennogo prostranstva nad kompleksnym proektivnym prostranstvom”, Matem. sb., 103(145):4(8) (1977), 505–518 | MR | Zbl

[7] Plemelj J., “Riemannsche Formenscharen mit gegebener Monodromiegruppe”, Mh. Math., 1908, 211–246 | MR | Zbl

[8] Röhrl H., “Das Riemann–Hilbertsche Problem der Theorie der linearen Differentialgleichungen”, Math. Ann., 133 (1957), 1–25 | DOI | MR | Zbl

[9] Nastold H. J., “Über meromorphe Schnitte komplex-analytischer Vektorraumbundel und Anwendungen auf Riemannsche Klassen”, Math. Z., 70 (1958), 55–92 | DOI | MR | Zbl

[10] Levelt A. H. M., “Hypergeometric functions”, Nederl. Akad. Wetensch. Proc. Ser. A 64 = Indag. Math., 23 (1961), 190–211

[11] Weil A., “Généralization des fonctions abéliennes”, J. Math. Pures et Appl., 17 (1938), 47–87 | Zbl

[12] Atiyah M. F., “Complex analytic connections in fibre bundles”, Trans. Amer. Math. Soc., 85:1 (1957), 181–207 | DOI | MR | Zbl

[13] Grothendieck A., “Sur le mémoire de Weil: généralisation des fonctions abéliennes”, Séminaire Bourbaki, Vol. 4, Soc. Math. France, Paris, 1995, 57–71, Exp. 141 | MR

[14] Lappo-Danilevskii I. A., Primenenie funktsii ot matrits k teorii lineinykh sistem obyknovennykh differentsialnykh uravnenii, Gostekhizdat, M., 1957

[15] Markov A. A., Osnovy algebraicheskoi teorii kos, Trudy Matem. instituta im. V. A. Steklova AN SSSR, 16, AN SSSR, 1945 | MR | Zbl

[16] Lin V. Ya., “Kosy Artina i svyazannye s nimi gruppy i prostranstva”, Itogi nauki i tekhn. Ser. Algebra, topol., geom., 17, VINITI, M., 1979, 159–227 | MR | Zbl

[17] Fox R., Neuwirth L., “The braid groups”, Math. Scand., 10 (1962), 119–126 | MR | Zbl

[18] Hattori A., “Topology of $C^n$ minus a finite number of affine hyperplanes in general position”, J. Fac.Sci. Univ. Tokyo, 22 (1975), 205–219 | MR | Zbl

[19] Golubeva V. A., “O fuksovykh sistemakh differentsialnykh uravnenii na kompleksnom proektivnom prostranstve”, Differents. uravneniya, XIII:9 (1977), 1570–1580 | MR

[20] Gárard R., Levelt A. H. M., “Etude d'une classe particuliere de systjemes de Pfaff du type de Fuchs sur l'espace projectif complexe”, J. Math. Pures et Appl., 51 (1972), 189–217 | MR

[21] Vasilevich N. D., Ladis N. N., “Integriruemost uravnenii Pfaffa na $CP^n$”, Differents. uravneniya, 15:4 (1979), 732–733 | MR | Zbl

[22] Essen van den A., “Reduction of singularities of the differential equation $Ady=Bdx$. Equations differentielles et systèmes de Pfaff dans le champ complexe” (Sem. Inst. Rech. Math. Avancée, Strasbourg, 1975), Lecture Notes in Math., 712, Springer, Berlin, 1979, 44–59 | MR

[23] Chen K. T., “Iterated path integrals”, Bull. Amer. Math. Soc., 83:5 (1977), 831–879 | DOI | MR | Zbl

[24] Aomoto K., “On the acyclity of free cobar construction. I”, Proc. Japan Acad. (A), 53:1 (1977), 35–36 ; “II”:2, 79 | DOI | MR | Zbl | Zbl

[25] Parshin A. N., “Ob odnom obobschenii yakobieva mnogoobraziya”, Izv. AN SSSR. Ser. matem., 30:1 (1966), 175–182 | MR | Zbl

[26] Otsuki M., “A residue formula for Chern classes associated with logarithmic connections”, Proc. Japan Acad. Ser. A, 54:9 (1978), 295–297 | DOI | MR | Zbl

[27] Aomoto K., “Fonctions hyperlogarithmique et groupes de monodromie unipotents”, J. Fac. Sci. Univ. Tokyo, Ser. IA, 25:2 (1978), 149–156 | MR | Zbl

[28] Leksin V. P., “Lineinye matrichnye uravneniya s nilpotentnoi monodromiei”, Geometricheskie metody v zadachakh analiza i algebry, Yaroslavskii universitet, 1978, 121–129 | MR | Zbl

[29] Deligne P., Equations différentielles á points singuliers réguliers, Lecture Notes in Math., Springer, Berlin, Heidelberg, New York, 1970, 163 pp. | MR | Zbl

[30] Katz N., “An overview of Deligne's work on Hilbert twentyfirst problem”, Proc. Symp. in pure math. Amer. Math. Soc., 28 (1976), 537–557 | MR | Zbl