Introduction to Singularities and Deformations

This book presents the basic singularity theory of analytic spaces, including local deformation theory, and the theory of plane curve singularities. The authors develop the relevant techniques, including the Weierstraß preparation theorem, the finite coherence theorem, etc., and then discuss isolated hypersurface and plane curve singularities, including the finite determinacy, classification of simple singularities, topological and analytic invariants, and resolution. In the local deformation theory emphasis is placed on the issues of the versality, obstructions, and equisingular deformations. The book includes a thorough treatment of equisingular deformations of plane curve singularities including a proof for the smoothness of the mu-constant stratum based on deformations of the parametrization.