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Some Open Problems in Complex Singularities

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

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

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Abstract

We discuss some open problems and questions related with five different topics in complex singularities. These are: (i) Topological and holomorphic ranks of an isolated singularity germ and the Zariski-Lipman conjecture; (ii) Graph manifolds and links of surface singularities. (iii) Milnor’s fibration for complex singularities and the topology of analytic foliations near an isolated singularity. (iv) Rochlin’s signature theorem and Gorenstein surface singularities. (v) The index of a vector field on a singular variety. These are all topics on which I have been interested for a long time.

Thanks: Partially supported by CONACYT, Mexico, and PAPIIT-UNAM project IN 101114

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Authors and Affiliations

  1. Instituto de Matemáticas, Universidad Nacional Autónoma de México, Mexico City, Mexico

    José Seade

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  1. José Seade
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Correspondence to José Seade .

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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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Seade, J. (2018). Some Open Problems in Complex Singularities. 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_14

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