Families of curves over \(\mathbb P^1\) with 3 singular fibers
type: Item
instance of: scholarly article
title: Families of curves over \(\mathbb P^1\) with 3 singular fibers
zbMATH Open document ID: 1282.14063
author: Cheng Gong
author: Xin Lu
author: Sheng-Li Tan
published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris
publication date: 2013-07-30T00:00:00Z
review text: Nontrivial semistable families of curves with minimal number of singular fibers have remarkable arithmetic and geometric properties. In the paper under review, the authors consider a relatively minimal genus \(g\) fibration \(S\) over \(\mathbb P^1\) with \(3\) singular fibers, \(2\) of which are semistable. They prove that \(S\) is a rational surface, the Mordell-Weil group is finite, and \(2g\leq -K_S^2 \leq 4g-4\). For \(g=2^n\), they construct examples to show that such fibrations exist.
reviewed by: Dawei Chen
Mathematics Subject Classification ID: 14J25
Mathematics Subject Classification ID: 14D06
Mathematics Subject Classification ID: 14H10
zbMATH DE Number: 6192617
zbMATH Keywords: family of curves
zbMATH Keywords: semistable fiber
zbMATH Keywords: rational surface
MaRDI profile type: Publication
full work available at URL: j.crma.2013.05.002
OpenAlex ID: W1967168526
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DOI: 10.1016/J.CRMA.2013.05.002
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description: scientific article; zbMATH DE number 6192617