On Galois group of factorized covers of curves
type: Item
instance of: scholarly article
title: On Galois group of factorized covers of curves
zbMATH Open document ID: 1498.14080
author: Angel Carocca
author: Martha Romero Rojas
published in: Revista Matemática Iberoamericana
publication date: 2019-02-14T00:00:00Z
review text: Summary: Let \(\mathcal{Y} \mathop{\rightarrow}\limits^{\psi}\mathcal{X} \mathop{\rightarrow}\limits^{\varphi} \mathbb{P}^{1}\) be a sequence of covers of compact Riemann surfaces. In this work we study and completely characterize the Galois group \(\mathfrak{G}(\phi\circ\psi)\) of \(\phi\circ\psi\) under the following properties: \(\phi\) is a simple cover of degree \(m\) and \(\psi\) is a Galois unramified cover of degree \(n\) with abelian Galois group of type \((n_1,n_2,\dots,n_s)\). We prove that \( \mathfrak{G}(\phi\circ\psi) \cong ({\mathbb Z}_{n_1} \times {\mathbb Z}_{n_2} \times \cdots \times {\mathbb Z}_{ns})^{m-1} \rtimes {\mathbf S}_m\). Furthermore, we give a natural geometric generator system of \(\mathfrak{G}(\phi\circ\psi)\) obtained by studying the action on the compact Riemann surface \(\mathcal{Z}\) associated to the Galois closure of \(\phi\circ\psi.\)
Mathematics Subject Classification ID: 14H37
Mathematics Subject Classification ID: 14H55
zbMATH DE Number: 7023581
zbMATH Keywords: covers
zbMATH Keywords: Riemann surfaces
zbMATH Keywords: monodromy
zbMATH Keywords: automorphisms
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.4171/rmi/1046
OpenAlex ID: W2905404985
cites work: Monodromy groups of Hurwitz-type problems
cites work: Q3582303
cites work: Algebraic functions with even monodromy
cites work: Irreducibility of Moduli Spaces of Cyclic Unramified Covers of Genus g Curves
cites work: Classifying finite group actions on surfaces of low genus
cites work: Products of Jacobians as Prym-Tyurin varieties
cites work: The groups determined by the relations \(s^l=T^m=(S^{-1}T^{-1}ST)^p=1\). I
cites work: Every curve is a Hurwitz space
cites work: Q3481848
cites work: Q4849451
cites work: Symmetric and alternating groups as monodromy groups of Riemann surfaces. I. Generic covers and covers with many branch points
cites work: Hurwitz spaces of Galois coverings of \(\mathbb P^1\), whose Galois groups are Weyl groups
cites work: Applied finite group actions.
cites work: The monodromy group of a function on a general curve
cites work: Group actions on Jacobian varieties
cites work: Q5438051
cites work: Q3890809
DOI: 10.4171/RMI/1046
description: scientific article; zbMATH DE number 7023581