Wild quotients of products of curves
type: Item
instance of: scholarly article
title: Wild quotients of products of curves
zbMATH Open document ID: 1401.14023
published in: European Journal of Mathematics
publication date: 2018-07-31T00:00:00Z
review text: Let \(k\) be an algebraically closed field of characteristic \(p>0\) and \(X_1, X_2\) be two smooth proper connected curves. Let \(\sigma_i: X_i\to X_i\) be an automorphism of order \(p\) and denote by \(\sigma\) the automorphism \(\sigma_1\times \sigma_2: X_1\times X_2\to X_1\times X_2=:Y\). It is proved that the graph of the resolution of any singularity of \(Y/\langle\sigma \rangle\) is a star-shaped graph with three terminal chains when \(X_2\) is an ordinary curve of positive genus. The intersection matrix of the resolution has determinant \(\pm p^2\). The singularity is rational. It is proved that for any \(s>0\) not divisible by \(p\) there are resolution graphs of wild \(\mathbb{Z}/p\mathbb{Z}\) quotient singularities with one node, \(s+2\) terminal chains and intersection matrix having determinant \(\pm p^{s+1}\).
reviewed by: Gerhard Pfister
Mathematics Subject Classification ID: 14B05
Mathematics Subject Classification ID: 14G20
Mathematics Subject Classification ID: 14E15
Mathematics Subject Classification ID: 14H20
Mathematics Subject Classification ID: 13H15
Mathematics Subject Classification ID: 14J17
zbMATH DE Number: 6911824
zbMATH Keywords: product of curves
zbMATH Keywords: cyclic quotient singularity
zbMATH Keywords: rational singularity
zbMATH Keywords: wild
zbMATH Keywords: intersection matrix
zbMATH Keywords: resolution graph
zbMATH Keywords: fundamental cycle
author: Dino Lorenzini
MaRDI profile type: Publication
full work available at URL: s40879-017-0174-0
OpenAlex ID: W2749340292
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DOI: 10.1007/S40879-017-0174-0
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description: scientific article; zbMATH DE number 6911824