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Izv. Akad. Nauk SSSR Ser. Mat., 1985, Volume 49, Issue 4, Pages 705–718 (Mi izv2388)  

On systems with regular singularities, and their solutions

V. A. Golubeva


Abstract: In this article two problems are solved.
1. It is shown that there exists an exponential representation for the fundamental matrix of a Pfaffian system on $C^n$ with regular singularities on a reducible algebraic submanifold $L$.
2. Let there be given on an algebraic manifold $X$ a function $f(x)$ of the Nilsson class with branch manifold $L\subset X$. It is shown that in a neighborhood of an ordinary point or of a point of normal intersection of components of $L$ the function $f(x)$ generates a $\mathscr D_X$-module with regular singularities on $L$.
Bibliography: 28 titles.

Full text: PDF file (2153 kB)
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English version:
Mathematics of the USSR-Izvestiya, 1986, 27:1, 27–38

Bibliographic databases:

UDC: 517.589
MSC: Primary 58A17; Secondary 81C30, 32B30
Received: 23.09.1982

Citation: V. A. Golubeva, “On systems with regular singularities, and their solutions”, Izv. Akad. Nauk SSSR Ser. Mat., 49:4 (1985), 705–718; Math. USSR-Izv., 27:1 (1986), 27–38

Citation in format AMSBIB
\Bibitem{Gol85}
\by V.~A.~Golubeva
\paper On systems with regular singularities, and their solutions
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1985
\vol 49
\issue 4
\pages 705--718
\mathnet{http://mi.mathnet.ru/izv2388}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=806681}
\zmath{https://zbmath.org/?q=an:0601.58007|0589.58001}
\transl
\jour Math. USSR-Izv.
\yr 1986
\vol 27
\issue 1
\pages 27--38
\crossref{https://doi.org/10.1070/IM1986v027n01ABEH001163}


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  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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