On equimultiple subschemes of a local scheme over a field of characteristic zero (Q1080899)

Let X be the spectrum of a quasi-unmixed local Nagata ring over a field of characteristic zero, and let Y be a reduced closed subscheme of X. The main result of the paper is the following: if x is the closed point of X and if X is equimultiple along Y, then the embedding dimension of Y at x is less than or equal to dim(X). Then the author applies this result to get a stability theorem for standard bases and a structure theorem for tangent cones.