Calculating the fundamental group of Galois cover of the (2,3)-embedding of \(\mathbb{CP}^1 \times T\)
type: Item
instance of: scholarly article
title: Calculating the fundamental group of Galois cover of the (2,3)-embedding of \(\mathbb{CP}^1 \times T\)
zbMATH Open document ID: 1477.14086
author: Meirav Amram
author: Michael Yoshpe
author: Sheng-Li Tan
author: Wan-Yuan Xu
publication date: 2020-04-15T00:00:00Z
review text: In the paper under review, the authors investigate the fundamental group of the Galois cover of the \((2,3)\)-embedding of \(X:=\mathbb{P}^{1}_{\mathbb{C}} \times T\), where \(T\) is a complex torus in \(\mathbb{P}^{2}_{\mathbb{C}}\). More precisely, since \(\mathbb{P}^{1}_{\mathbb{C}}\) can be embedded into \(\mathbb{P}^{m}_{\mathbb{C}}\) with \(m\geq 2\) and \(T\) can be embedded into \(\mathbb{P}^{n-1}_{\mathbb{C}}\) with \(n\geq 3\), then \(\mathbb{P}^{1}_{\mathbb{C}} \times T\) can be embedded into a larger projective space by the Segre embedding of \(\mathbb{P}^{m}_{\mathbb{C}} \times \mathbb{P}^{n-1}_{\mathbb{C}}\). Such an embedding is the \((m,n)\)-embedding of \(\mathbb{P}^{1}_{\mathbb{C}} \times T\) and one denotes the image of the embedding by \(X_{m,n}\). The resulting surface is of general type with index zero. In order to investigate the fundamental group, the authors apply Moishezon-Teicher's algorithm combined with certain degeneration techniques.
reviewed by: Piotr Pokora
Mathematics Subject Classification ID: 14N20
Mathematics Subject Classification ID: 14F35
Mathematics Subject Classification ID: 14J29
Mathematics Subject Classification ID: 14Q10
Mathematics Subject Classification ID: 20F36
Mathematics Subject Classification ID: 32S22
Mathematics Subject Classification ID: 52C35
Mathematics Subject Classification ID: 14H20
zbMATH DE Number: 7189516
zbMATH Keywords: fundamental groups
zbMATH Keywords: Galois cover
zbMATH Keywords: braid monodromy factorization
MaRDI profile type: Publication
full work available at URL: s10114-020-9220-9
OpenAlex ID: W3009343542
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DOI: 10.1007/S10114-020-9220-9
published in: Acta Mathematica Sinica, English Series
description: scientific article; zbMATH DE number 7189516