A new proof of desingularization over fields of characteristic zero.

Encinas, Santiago, and Villamayor, Orlando. "A new proof of desingularization over fields of characteristic zero.." Revista Matemática Iberoamericana 19.2 (2003): 339-353. <http://eudml.org/doc/39705>.

@article{Encinas2003,
abstract = {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 (see also [171 page 224). Given a subscheme defined by equations, we prove that embedded desingularization can be achieved by a sequence of monoidal transformations; where the law of transformation on the equations defining the subscheme is simpler then that used in Hironaka 's procedure. This 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. This provides a conceptual simplification of the original proof of Hironaka. This algorithm of principalization (of Logresolution of ideals), and this new procedure of embedded desingularization discussed here, have been implemented in MAPLE.},
author = {Encinas, Santiago, Villamayor, Orlando},
journal = {Revista Matemática Iberoamericana},
keywords = {Geometría algebraica; Singularidades},
language = {eng},
number = {2},
pages = {339-353},
title = {A new proof of desingularization over fields of characteristic zero.},
url = {http://eudml.org/doc/39705},
volume = {19},
year = {2003},
}

TY - JOUR
AU - Encinas, Santiago
AU - Villamayor, Orlando
TI - A new proof of desingularization over fields of characteristic zero.
JO - Revista Matemática Iberoamericana
PY - 2003
VL - 19
IS - 2
SP - 339
EP - 353
AB - 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 (see also [171 page 224). Given a subscheme defined by equations, we prove that embedded desingularization can be achieved by a sequence of monoidal transformations; where the law of transformation on the equations defining the subscheme is simpler then that used in Hironaka 's procedure. This 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. This provides a conceptual simplification of the original proof of Hironaka. This algorithm of principalization (of Logresolution of ideals), and this new procedure of embedded desingularization discussed here, have been implemented in MAPLE.
LA - eng
KW - Geometría algebraica; Singularidades
UR - http://eudml.org/doc/39705
ER -