Geodesic
A meromorphic section of a complex analytic vector bundle over complex projective space
Sbornik. Mathematics, Tome 32 (1977) no. 4, pp. 437-447 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The Riemann–Hilbert problem on a complex analytic manifold $V$ is as follows. Consider an analytic submanifold $L$ of codimension 1 in $V$ and a representation $\chi\colon\pi_1(V-L,x_0)\to GL(m,C)$. Does there exist a Pfaffian system of Fuchs type on $V$ whose solution space realizes the representation $\chi$? This paper is devoted to the study of conditions for the solvability of the Riemann–Hilbert problem on $CP^n$ with a given reducible algebraic variety of codimension 1 on it, whose irreducible components are nonsingular and cross each other normally. Bibliography: 15 titles. 
@article{SM_1977_32_4_a3,
     author = {V. A. Golubeva},
     title = {A~meromorphic section of a~complex analytic vector bundle over complex projective space},
     journal = {Sbornik. Mathematics},
     pages = {437--447},
     year = {1977},
     volume = {32},
     number = {4},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1977_32_4_a3/}
}
TY  - JOUR
AU  - V. A. Golubeva
TI  - A meromorphic section of a complex analytic vector bundle over complex projective space
JO  - Sbornik. Mathematics
PY  - 1977
SP  - 437
EP  - 447
VL  - 32
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/SM_1977_32_4_a3/
LA  - en
ID  - SM_1977_32_4_a3
ER  - 
%0 Journal Article
%A V. A. Golubeva
%T A meromorphic section of a complex analytic vector bundle over complex projective space
%J Sbornik. Mathematics
%D 1977
%P 437-447
%V 32
%N 4
%U http://geodesic.mathdoc.fr/item/SM_1977_32_4_a3/
%G en
%F SM_1977_32_4_a3
V. A. Golubeva. A meromorphic section of a complex analytic vector bundle over complex projective space. Sbornik. Mathematics, Tome 32 (1977) no. 4, pp. 437-447. http://geodesic.mathdoc.fr/item/SM_1977_32_4_a3/

[1] F. Fam, Osobennosti protsessov mnogokratnogo rasseyaniya, izd-vo «Mir», Moskva, 1972 | MR

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

[3] R. Gérard, A. H. M. Levelt, “Étude d'une classe particulière de systèmes de Pfaff du type de Fuchs sur l'espace projectif complexe”, J. math. pures et appl., 51 (1972), 189–217 | MR

[4] A. Bolibrukh, “Sistemy Pfaffa tipa Fuksa na kompleksnom proektivnom prostranstve”, Matem. sb., 103 (145) (1977), 112–123 | Zbl

[5] R. Gérard, “Le problème de Riemann - Hilbert sur une varieté analytique complexe”, Ann. Inst. Fourier, 19:2 (1969), 1–32 | MR | Zbl

[6] A. Weil, “Sur la théorie des formes différentielles attachées a une varieté analytique complexe”, Comm. Math. Helv., 20 (1947), 110–116 | DOI | MR | Zbl

[7] A. Weil, “Généralisation des fonctions abéliennes”, J. math. pures et appl., 17 (1938), 47–87 | Zbl

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

[9] H. J. Nastold, “Über meromorphe Schnitte komplex-analytischer Vektorraumbundel und Anwendungen auf Riemannschen Klassen”, Math. Z., 69 (1958), 366–394 | DOI | MR | Zbl

[10] I. A. Lappo-Danilevskii, Primenenie funktsii ot matrits k teorii lineinykh sistem obyknovennykh differentsialnykh uravnenii, Gostekhizdat, Moskva, 1957 | MR

[11] A. Borel, Lineinye algebraicheskie gruppy, izd-vo «Mir», Moskva, 1972 | MR

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

[13] P. Delin, “Teoriya Khodzha, II”, Matematika, 17:5 (1973), 3–56 | MR

[14] P. Deligne, Équations différentielles à points singuliers réguliers, Lecture Notes in Math., 163, Springer-Verlag, Berlin–New York, 1970 | MR | Zbl

[15] S. Nakano, “On complex analytic vector bundles”, J. Math. Soc. Japan, 7:1 (1957), 1–12 | MR