Geodesic
Pfaffian systems of Fuchs type on a complex analytic manifold
Sbornik. Mathematics, Tome 32 (1977) no. 1, pp. 98-108 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

In this paper we give necessary and sufficient conditions for a completely integrable Pfaffian system with regular singular points on $A$ to be a Fuchsian system, where $A$ is a divisor with normal crossings in a compact Kähler manifold $W^m$. We prove that the condition of being a Fuchsian system is equivalent to the solvability of some first Cousin problem on $W^m$. This condition appears particularly simple when $W^m$ is complex projective space. Bibliography: 12 titles. 
@article{SM_1977_32_1_a5,
     author = {A. A. Bolibrukh},
     title = {Pfaffian systems of {Fuchs} type on a~complex analytic manifold},
     journal = {Sbornik. Mathematics},
     pages = {98--108},
     year = {1977},
     volume = {32},
     number = {1},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1977_32_1_a5/}
}
TY  - JOUR
AU  - A. A. Bolibrukh
TI  - Pfaffian systems of Fuchs type on a complex analytic manifold
JO  - Sbornik. Mathematics
PY  - 1977
SP  - 98
EP  - 108
VL  - 32
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/SM_1977_32_1_a5/
LA  - en
ID  - SM_1977_32_1_a5
ER  - 
%0 Journal Article
%A A. A. Bolibrukh
%T Pfaffian systems of Fuchs type on a complex analytic manifold
%J Sbornik. Mathematics
%D 1977
%P 98-108
%V 32
%N 1
%U http://geodesic.mathdoc.fr/item/SM_1977_32_1_a5/
%G en
%F SM_1977_32_1_a5
A. A. Bolibrukh. Pfaffian systems of Fuchs type on a complex analytic manifold. Sbornik. Mathematics, Tome 32 (1977) no. 1, pp. 98-108. http://geodesic.mathdoc.fr/item/SM_1977_32_1_a5/

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

[2] V. A. Golubeva, “Nekotorye voprosy analiticheskoi teorii feinmanovskikh integralov”, Uspekhi matem. nauk, XXXI:2 (188) (1976), 135–202 | MR

[3] A. H. M. Levelt, “Hypergeometric functions”, Indag. Math., XXIII:4 (1961), 361–401 | MR

[4] Zh. Lere, Differentsialnoe i integralnoe ischisleniya na kompleksnom analiticheskom mnogoobrazii, IL, Moskva, 1961

[5] H. J. Nastold, “Über meromorphe Schnitte komplexe analytischer Vektorraumbündel und Anwendungen auf Riemannsche Klassen, II”, Math. Z., 70:1 (1958), 55–92 | DOI | MR | Zbl

[6] G. de Rham, K. Kodaira, Harmonic integrals, preprint, 1954 | Zbl

[7] M. Yoshida, K. Takano, “Local theory of fuchsian systems, I”, Proc. Japan Acad., LI:4 (1975), 219–223 | DOI | MR

[8] Chzhen Shen-shen, Kompleksnye mnogoobraziya, IL, Moskva, 1961