From Singularities to Graphs

Patrick Popescu-Pampu ()
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Patrick Popescu-Pampu: UMR 8524 - Laboratoire Paul Painlevé, University of Lille, CNRS

A chapter in When Form Becomes Substance, 2022, pp 231-263 from Springer

Abstract: Abstract In this text I present some problems which led to the introduction of special kinds of graphs as tools for studying singular points of algebraic surfaces. I explain how such graphs were first described using words, and how several classification problems made it necessary to draw them, leading to the elaboration of a special kind of calculus with graphs. This non-technical paper is intended to be readable both by mathematicians and philosophers or historians of mathematics.

Keywords: Coxeter diagrams; Dual graphs; Du Val singularities; Graph manifolds; Models of surfaces; Plumbing calculus; Resolution of singularities; Singularity links; Surface singularities; 14B05 (primary); 32S25; 32S45; 32S50; 57M15; 01A60 (search for similar items in EconPapers)
Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-030-83125-7_8

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DOI: 10.1007/978-3-030-83125-7_8

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