On the moduli spaces of fiber bundles of curves of genus \(\geqq 2\)
type: Item
instance of: scholarly article
title: On the moduli spaces of fiber bundles of curves of genus \(\geqq 2\)
zbMATH Open document ID: 0988.14016
author: Hurşit Önsiper
published in: Archiv der Mathematik
publication date: 2001-07-05T00:00:00Z
review text: Let \(X\to S\) be an analytic fiber bundle with fiber \(F\) of genus \(g\geq 2\) over a curve of genus \(g_b\). Let \(K^2=8(g_b-1) (g-1)\) and \(\chi= (g_b-1) (g-1)\). The aim of this paper is to study the subvariety parametrizing these fiber bundles in the moduli space \({\mathcal M}_{K^2,\chi}\) of surfaces of general type. The author proves the following theorem: If \(g_b> (g+1)/2\), then the connected component \({\mathcal M}\) of \({\mathcal M}_{K^2,\chi}\) containing the modulus of \(X\), parametrizes precisely the surfaces admitting analytic fiber bundle structure with the same \(g,g_b\) and \({\mathcal G}\) where \({\mathcal G}=\text{Image} (\pi_1(S) \to\Aut (F))\).
Mathematics Subject Classification ID: 14J10
Mathematics Subject Classification ID: 14D20
Mathematics Subject Classification ID: 14H10
zbMATH DE Number: 1556586
zbMATH Keywords: fiber bundles
zbMATH Keywords: surfaces of general type
zbMATH Keywords: moduli space
reviewed by: A. Del Centina
MaRDI profile type: Publication
full work available at URL: s000130050514
OpenAlex ID: W2105603074
DOI: 10.1007/S000130050514
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description: scientific article; zbMATH DE number 1556586