Sextic curves with simple singularities
type: Item
instance of: scholarly article
title: Sextic curves with simple singularities
zbMATH Open document ID: 0866.14014
author: Jingen Yang
published in: Tôhoku Mathematical Journal. Second Series
publication date: 1997-07-24T00:00:00Z
review text: In this paper the author studies the configuration of simple singularities in a reduced sixtic curve in \(\mathbb{P}^2\). Recall that singularities are described by their dual graph in an embedded resolution of singularities and simple singularities are in correspondence with simple Dynkin diagrams, of type \(A_i\) \((i\geq 1)\), \(D_j\) \((j\geq 4)\) and \(E_k\) \((k=6,7,8)\). The main theorem in this article is: There exists a reduced sixtic curve in \(\mathbb{P}^2\) with only simple singularities given by a finite Dynkin graph \(G\) if and only if \(G\) is a subgraph of a graph listed by the author. For the proof the author uses full version of Nikulin's embedding theorem of even lattices.
Mathematics Subject Classification ID: 14H20
Mathematics Subject Classification ID: 14E15
Mathematics Subject Classification ID: 14Q05
zbMATH DE Number: 927276
zbMATH Keywords: resolution of singularities
zbMATH Keywords: Dynkin diagrams
zbMATH Keywords: sixtic curve
reviewed by: Marcel Morales
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2748/tmj/1178225377
OpenAlex ID: W2043747235
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DOI: 10.2748/TMJ/1178225377
description: scientific article; zbMATH DE number 927276