# A new proof of desingularization over fields of characteristic zero.

Santiago Encinas; Orlando Villamayor

Revista Matemática Iberoamericana (2003)

- Volume: 19, Issue: 2, page 339-353
- ISSN: 0213-2230

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topEncinas, 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 -

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