Rings of singularities
type: Item
instance of: scholarly article
title: Rings of singularities
zbMATH Open document ID: 1262.14042
author: Helmut Lenzing
published in: Bulletin of the Iranian Mathematical Society
publication date: 2012-11-16T00:00:00Z
review text: This is a lecture note on singularity theory. It is shown how to associate to a triple of positive integers \((p_1,p_2,p_3)\) a two-dimensional isolated graded singularity by an elementary procedure that works over any field \(k\) (with no assumptions on characteristic, algebraic closedness or cardinality). This assignment starts from the triangle singularity \(x_1^{p_1} + x_2^{p_2} + x_3^{p_3}\) and when applied to the Platonic (or Dynkin) triples, it produces the famous list of A-D-E-singularities. As another particular case, the procedure yields Arnold's famous strange duality list consisting of the 14 exceptional unimodular singularities (and an infinite sequence of further singularities not treated here in detail). It is shown that weighted projective lines and various triangulated categories attached to them play a key role in the study of the triangle and associated singularities.
Mathematics Subject Classification ID: 14J17
Mathematics Subject Classification ID: 16G20
Mathematics Subject Classification ID: 16G50
zbMATH DE Number: 6108069
zbMATH Keywords: weighted projective line
zbMATH Keywords: (extended) canonical algebra
zbMATH Keywords: simple singularity
zbMATH Keywords: Arnold's strange duality
zbMATH Keywords: stable category of vector bundles
reviewed by: Huang Hua-Lin
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 6108069