Introduction to Singularities and Deformations

摘要: Singularity theory is a field of intensive study in modern mathematics with fascinating relations to algebraic geometry, complex analysis, commutative algebra, representation theory, Lie groups, topology, dynamical systems, and many more, numerous applications the natural technical sciences. This book presents basic singularity analytic spaces, including local deformation plane curve singularities. Plane singularities are classical object study, rich ideas applications, which still center current research as such provides an ideal introduction general theory. Deformation important technique branches contemporary geometry analysis. This introductory text framework while remaining concrete. In first part authors develop relevant techniques, Weierstras preparation theorem, finite coherence theorem etc., then treat isolated hypersurface singularities, notably determinacy, classification simple topological invariants. In emphasis laid on issues versality, obstructions, equisingular deformations. The moreover contains new treatment deformations proof for smoothness mu-constant stratum based parameterization. Computational aspects discussed well. Three appendices, facts from sheaf formal make reading self-contained. The material, can be found partly other books articles, presented unified point view time. It given complete proofs, cases. thus serve source special courses geometry.