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Funktsional. Anal. i Prilozhen., 2011, Volume 45, Issue 3, Pages 55–78 (Mi faa3040)  

This article is cited in 1 scientific paper (total in 1 paper)

Algebraic functions, configuration spaces, Teichmüller spaces, and new holomorphically combinatorial invariants

V. Ya. Lin

1.Technion-Israel institute of Technology, Haifa, Israel

Abstract: It is proved that, for $n\ge 4$, the function $u=u_n(z)$, $z=(z_1,…,z_n)\in{\mathbb{C}}^n$, defined by the equation $u^n +z_1 u^{n-1} +…+ z_n=0$ cannot be a branch of an entire algebraic function $g$ on ${\mathbb{C}}^n$ that is a composition of entire algebraic functions depending on fewer than $n-1$ variables and has the same discriminant set as $u_n$. A key role is played by a description of holomorphic maps between configuration spaces of ${\mathbb{C}}$ and ${\mathbb{CP}}^1$, which, in turn, involves Teichmüller spaces and new holomorphically combinatorial invariants of complex spaces.

Keywords: configuration spaces, braid groups, compositions of algebraic functions, invariants of complex spaces.

DOI: https://doi.org/10.4213/faa3040

Full text: PDF file (393 kB)
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English version:
Functional Analysis and Its Applications, 2011, 45:3, 204–224

Bibliographic databases:

UDC: 515.162.8+515.17+515.172+512.54
Received: 16.03.2011

Citation: V. Ya. Lin, “Algebraic functions, configuration spaces, Teichmüller spaces, and new holomorphically combinatorial invariants”, Funktsional. Anal. i Prilozhen., 45:3 (2011), 55–78; Funct. Anal. Appl., 45:3 (2011), 204–224

Citation in format AMSBIB
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    This publication is cited in the following articles:
    1. Florence M., Reichstein Z., “The Rationality Problem For Forms of M<Overbar></Mml:Mover>0<Mml:Mo>,N”, Bull. London Math. Soc., 50:1 (2018), 148–158  crossref  mathscinet  zmath  isi  scopus
  • Функциональный анализ и его приложения Functional Analysis and Its Applications
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