Can anyone recommend a good overview of singularity theory? In particular, quotient singularities...
Thanks!
Can anyone recommend a good overview of singularity theory? In particular, quotient singularities... Thanks! 


Golubitsky and Guillemin Stable Mappings and their singularities is a fairly canonical reference for the ThomMatherLevine thread of ideas, building off of Whitney and Morse's work. 


Perhaps Young person's guide to canonical singularities by Miles Reid. The connection seems to be that at least for surfaces, canonical singularities are exactly quotient singularities by finite subgroups of SL(2,C), (rational double points). In higher dimension the two types no longer coincide. I am a novice, and merely repeating what I have noted from browsing. 


If you are looking for a more topological treatment of the subject, there is a twovolume Singularities of Differentiable Maps by Arnold, Varchenko and GuseinZade. 


Curves and Singularities by J.W. Bruce and P.J. Giblin gives a highly readable overview of basic singularity theory. 


A book I found very helpful was the book by János Kollár, named Lectures on Resolution of Singularities. In §2.3, he discusses Quotient Singularities, mostly in the context of resolution for surfaces. 

