Classification of unimodal parametric plane curve singularities in positive characteristic
type: Item
instance of: scholarly article
title: Classification of unimodal parametric plane curve singularities in positive characteristic
zbMATH Open document ID: 1548.58018
author: Muhammad Ahsan Binyamin
author: Gert-Martin Greuel
author: Khawar Mehmood
author: Gerhard Pfister
published in: Journal of Algebra
publication date: 2024-09-30T00:00:00Z
review text: After the inspiring paper by \textit{A. Hefez} and \textit{M. E. Hernandes} on Zariski's analytic classification of plane branches belonging to a given equisingularity class and [Bull. Lond. Math. Soc. 43, No. 2, 289--298 (2011; Zbl 1213.14056)], \textit{K. Mehmood} and \textit{G. Pfister} used it to classify unimodal plane branches in characteristic 0 [Bull. Math. Soc. Sci. Math. Roum., Nouv. Sér. 60(108), No. 4, 417--424 (2017; Zbl 1399.57008)].\N\NIn this paper, the authors give a complete classification of unimodal plane branches over an algebraically closed field of positive characteristic. The authors use a different approach and in some cases computer algebra. The main theoretical ingredients are semicontinuity of semigroups and modality.
Mathematics Subject Classification ID: 58K05
Mathematics Subject Classification ID: 14H20
zbMATH DE Number: 7920063
zbMATH Keywords: algebroid plane branches
zbMATH Keywords: parameterization
zbMATH Keywords: \( \mathcal{A} \)-equivalence
zbMATH Keywords: modality
zbMATH Keywords: classification
MaRDI profile type: Publication
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DOI: 10.1016/J.JALGEBRA.2024.07.018
description: scientific article; zbMATH DE number 7920063