Some properties of the Nash blowing-up

Augusto Nobile
1975 Pacific Journal of Mathematics  
A. NOBILE Intuitively, in the Nash blowing-up process each singular point of an algebraic (or analytic) variety is replaced by the limiting positions of tangent spaces (at non-singular points). The following properties of this process are shown: 1) It is, locally, a monoidal transform; 2) in characteristic zero, the process is trivial if and only if the variety is nonsingular. Examples show that this is not true in characteristic p >0; that, in general, the transform of a hypersurface is not
more » ... ally a hypersurface; and that this process does not give, in general, minimal resolutions.
doi:10.2140/pjm.1975.60.297 fatcat:e2hyfwt2efg7tbnzl3hamie6y4