A new proof of desingularization over fields of characteristic zero.

Título inglés A new proof of desingularization over fields of characteristic zero.
Título español Una nueva demostración de desingularización sobre campos de característica cero.
Autor/es Encinas, Santiago ; Villamayor, Orlando
Organización Dep. Mat. Apl. Fund. Esc. Téc. Super. Arquit. Univ. Valladolid, Valladolid, España;Dep. Mat. Univ. Autón. Madrid, Madrid, España
Revista 0213-2230
Publicación 2003, 19(2): 339-353, 29 Ref.
Tipo de documento articulo
Idioma Inglés
Resumen inglés 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.
Clasificación UNESCO 120101
Palabras clave español Geometría algebraica ; Singularidades
Código MathReviews MR2023188
Código Z-Math Zbl 1073.14021
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