Some Open Problems in Complex Singularities

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

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.

Keywords

Zariski-Lipman conjecture Graph manifolds Gorenstein singularities Milnor fibrations Foliations Rochlin signature theorem Indices of vector fields 

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Instituto de MatemáticasUniversidad Nacional Autónoma de MéxicoMexico CityMexico

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