On equimultiple subvarieties of algebroid hypersurfaces.

We deal with a finite projection piv of a hypersurface V in (r + 1)-space onto an affine r-space A(r) and with the critical variety Delta of piv in A(r). We show that if Delta is equimultiple along a smooth subvariety W(0), then W(0) admits a unique lifting to a subvariety W of V (necessarily isomorphic to W(0)) and that also V is then equimultiple along W.