2001/01/31 by S. Encinas, O. Villamayor
Mathematics · #math.AG #msc:14E15 #msc:32S45
published as Revista Matematica Iberoamericana 19, 339-353 (2003) · In accordance to the suggestions of referee: Title has changed and the structure of the paper is different. Proof of main theorem is clarified. Latex document, 11pages
arxiv created 2002/09/30 · arxiv updated 2009/11/30
We present a proof of embedded desingularization for closed subschemes which does not make use of Hilbert-Samuel function and avoids Hironaka's notion of normal flatness. This proof, already sketched in [A course on constructive desingularization and equivariance. In \em Resolution of singularities (Obergurgl, 1997), vol. 181 \em Progr. Math., Birkhäuser, 2000.] page 224, is done by showing that desingularization of a closed subscheme X, in a smooth sheme W, is achieved by taking an algorithmic principalization for the ideal I(X), associated to the embedded scheme X.