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Funktsional. Anal. i Prilozhen., 2003, Volume 37, Issue 2, Pages 65–74 (Mi faa149)  

This article is cited in 2 scientific papers (total in 2 papers)

On the Monodromy of a Multivalued Function Along Its Ramification Locus

A. G. Khovanskii

Institute of Systems Analysis, Russian Academy of Sciences

Abstract: We consider multivalued analytic functions in $\mathbb{C}^n$ whose set of singular points occupies a very small part of $\mathbb{C}^n$. Under a mapping of a topological space $Y$ into $\mathbb{C}^n$, such a function $f$ can induce a multivalued function on $Y$. This is possible even if the image of $Y$ entirely lies in the ramification set of $f$. We estimate the monodromy group of the induced function via the monodromy group of $f$.

Keywords: multivalued function, monodromy group, Galois theory

DOI: https://doi.org/10.4213/faa149

Full text: PDF file (165 kB)
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English version:
Functional Analysis and Its Applications, 2003, 37:2, 134–141

Bibliographic databases:

UDC: 517.9
Received: 26.11.2002

Citation: A. G. Khovanskii, “On the Monodromy of a Multivalued Function Along Its Ramification Locus”, Funktsional. Anal. i Prilozhen., 37:2 (2003), 65–74; Funct. Anal. Appl., 37:2 (2003), 134–141

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. A. G. Khovanskii, “On the Nonrepresentability of Functions of Several Variables by Quadratures”, Funct. Anal. Appl., 37:4 (2003), 302–310  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    2. A. G. Khovanskii, “On solvability and unsolvability of equations in explicit form”, Russian Math. Surveys, 59:4 (2004), 661–736  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
  • Функциональный анализ и его приложения Functional Analysis and Its Applications
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