Differential Forms on Zero-Dimensional Singularities

In this paper we discuss some problems of the deformation theory of zero-dimensional singularities, which are closely related to the study of properties of differential forms and the Poincaré–de Rham complex. We also investigate the cotangent homology and cohomology of zerodimensional singularities, compute the basic analytic invariants for certain types of such singularities, and examine in detail some interesting examples and applications.