Equisingularity and the Theory of Integral Closure

  • Terence GaffneyEmail author
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 222)


This is an introduction to the study of the equisingularity of sets using the theory of the integral closure of ideals and modules as the main tool. It introduces the notion of the landscape of a singularity as the right setting for equisingularity problems.


Equisingularity Multiplicity of ideals and modules Integral closure of ideals Integral closure of modules 



The author was partially supported by Conselho Nacional de Desenvolvimento Científico e Tecnológico - CNPq, Brazil, grant PVE 401565/2014-9. These lectures grew out of a short course of lectures given at the Universidade Federal Fluminense in January of 2015. It is pleasure to thank these institutions for their support. I also thank two individuals who had a strong impact on shaping my thinking on the subject–Steven Kleiman and Bernard Teissier. Their contributions to this work will be obvious to any serious reader. I also thank Steven Kleiman for several helpful comments which improved the exposition.


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Authors and Affiliations

  1. 1.Department of MathematicsNortheastern UniversityBostonUSA

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