A Proof of Desingularization over fields of characteristic zero

Details A Proof of Desingularization over fields of characteristic zero A Proof of Desingularization over fields of characteristic zero

2001-01-25

arxiv.org/abs/math/0101208v3

Revista Matematica Iberoamericana 19, 339-353 (2003)

Mathematics

Algebraic Geometry

In accordance to the suggestions of referee: Title has changed and the structure of the paper is different. Proof of main theo

Scientific paper

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.}, Birkh\"auser, 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 $X$.

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