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Equisingularity and the Theory of Integral Closure

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Book cover Singularities and Foliations. Geometry, Topology and Applications (NBMS 2015, BMMS 2015)

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 222))

Abstract

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.

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Acknowledgements

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. Department of Mathematics, Northeastern University, 567 Lake Hall, Boston, MA, 02115, USA

    Terence Gaffney

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  1. Terence Gaffney
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Correspondence to Terence Gaffney .

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Editors and Affiliations

  1. ICMC, University of São Paulo, São Carlos, São Paulo, Brazil

    Raimundo Nonato Araújo dos Santos

  2. Department of Mathematics, Federal University of Paraíba, João Pessoa, Paraíba, Brazil

    Aurélio Menegon Neto

  3. Mathematics Institute, University of Warwick, Coventry, United Kingdom

    David Mond

  4. ICMC, University of São Paulo, São Carlos, São Paulo, Brazil

    Marcelo J. Saia

  5. Instituto de Matemáticas, Unidad Cuernavaca, Universidad Nacional Autónoma de México, Cuernavaca, Morelos, Mexico

    Jawad Snoussi

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Gaffney, T. (2018). Equisingularity and the Theory of Integral Closure. In: Araújo dos Santos, R., Menegon Neto, A., Mond, D., Saia, M., Snoussi, J. (eds) Singularities and Foliations. Geometry, Topology and Applications. NBMS BMMS 2015 2015. Springer Proceedings in Mathematics & Statistics, vol 222. Springer, Cham. https://doi.org/10.1007/978-3-319-73639-6_3

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