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.
Zariski
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Department of Mathematics, Harvard University, Science Center, 1 Oxford Street, Cambridge, Massachusetts 02138.