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 |
Acceso al artículo completo |