Vol. 60, No. 1, 1975

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Some properties of the Nash blowing-up

Augusto Nobile

Vol. 60 (1975), No. 1, 297–305
Abstract

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 locally a hypersurface; and that this process does not give, in general, minimal resolutions.

Mathematical Subject Classification 2000
Primary: 14B10
Secondary: 32C45
Milestones
Received: 12 June 1974
Revised: 1 November 1974
Published: 1 September 1975
Authors
Augusto Nobile