Multiplicity of filtered rings and simple \(K3\) singularities of multiplicity two.
type: Item
instance of: scholarly article
title: Multiplicity of filtered rings and simple \(K3\) singularities of multiplicity two.
zbMATH Open document ID: 1056.14052
author: Masataka Tomari
published in: Publications of the Research Institute for Mathematical Sciences, Kyoto University
publication date: 2003-09-23T00:00:00Z
review text: Summary: Given a filtered ring, we give bounds of its multiplicity in terms of the data of the tangent cone using the technique of the filtered blowing-up. Applying it to each simple \(K3\) singularity of multiplicity two, we find a good coordinate where the Newton boundary of the defining equation contains the point \((1,1,1,1)\in\mathbb{R}^4\). In the course of the proof, we classify simple \(K3\) singularities of multiplicity two into 48 weight types. Furthermore, we prove that the weight type of the singularity stays the same under arbitrary one-parameter (FG)-deformations.
Mathematics Subject Classification ID: 14J17
Mathematics Subject Classification ID: 14B05
Mathematics Subject Classification ID: 14J28
zbMATH DE Number: 1902207
zbMATH Keywords: Newton boundary
zbMATH Keywords: (FG)-deformation
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2977/prims/1145476194
OpenAlex ID: W2078318365
DOI: 10.2977/PRIMS/1145476194
description: scientific article; zbMATH DE number 1902207