On the global monodromy of a fibration of the Fermat surface of odd degree \(n\)
type: Item
instance of: scholarly article
title: On the global monodromy of a fibration of the Fermat surface of odd degree \(n\)
zbMATH Open document ID: 1222.14016
author: Kazushi Ahara
author: Ikuko Awata
published in: Tokyo Journal of Mathematics
publication date: 2011-09-27T00:00:00Z
review text: Let \(M\) be a complex surface and \(B\) a complex curve. A holomorphic map \(f:M\rightarrow B\) is a degeneration map if it is proper, surjective, if there exist finitely many critical values \(s_i\in B\), \(i=1,\ldots ,r\) and if for \(s\neq s_i\) the fibre \(f^{-1}(s)\) is a compact Riemann surface. Fix a base point \(s_0\neq s_i\), \(i=1,\ldots ,r\). The global monodromy of the fibre \(f^{-1}(s_0)\) is a homomorphism \(\rho :\pi _1(B\backslash \{ s_i\},s_0)\rightarrow {\mathcal M}(f^{-1}(s_0))\), where \({\mathcal M}(f^{-1}(s_0))\) is a mapping class group of the fibre \(f^{-1}(s_0)\). The paper investigates the global topological monodromy of a certain fibration of the Fermat surface without using numerical analysis by computer.
Mathematics Subject Classification ID: 14D05
Mathematics Subject Classification ID: 14D06
zbMATH DE Number: 5950734
zbMATH Keywords: degeneration map
zbMATH Keywords: monodromy
reviewed by: Vladimir P. Kostov
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.3836/tjm/1313074444
OpenAlex ID: W2038980685
cites work: On the topology of Fermat type surface of degree 5 and the numerical analysis of algebraic curves
cites work: Subordinate fibers of Takamura splitting families for stellar singular fibers
cites work: On the global monodromy of a Lefschetz fibration arising from the Fermat surface of degree 4
cites work: On the topological structure of the Fermat surface of degree 5
cites work: Pseudo-periodic homeomorphisms and degeneration of Riemann surfaces
cites work: A proof of Thurston's uniformization theorem of geometric orbifolds
DOI: 10.3836/TJM/1313074444
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description: scientific article; zbMATH DE number 5950734