This article is cited in 4 papers

A meromorphic section of a complex analytic vector bundle over complex projective space

V. A. Golubeva


Abstract: 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.

UDC: 517.943.2

MSC: Primary 14D05, 32A30, 58A15, 34A20, 32L05; Secondary 30A88

Received: 21.01.1976

 English version: Mathematics of the USSR-Sbornik, 1977, 32:4, 437–447

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