Vol. 60, No. 1, 1975

Download this article
Download this article. For screen
For printing
Recent Issues
Vol. 323: 1
Vol. 322: 1  2
Vol. 321: 1  2
Vol. 320: 1  2
Vol. 319: 1  2
Vol. 318: 1  2
Vol. 317: 1  2
Vol. 316: 1  2
Online Archive
Volume:
Issue:
     
The Journal
Subscriptions
Editorial Board
Officers
Contacts
 
Submission Guidelines
Submission Form
Policies for Authors
 
ISSN: 1945-5844 (e-only)
ISSN: 0030-8730 (print)
Special Issues
Author Index
To Appear
 
Other MSP Journals
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