A new Proof of Desingularization over fields of characteristic zero
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Autores: Santiago Encinas Carrión
, Orlando E. Villamayor
- Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 19, Nº 2, 2003, págs. 339-353
- Idioma: inglés
- DOI: 10.4171/rmi/350
- Texto completo no disponible (Saber más ...)
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Resumen
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 \cite{EncinasVillamayor2000} 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 Log-resolution of ideals), and this new procedure of embedded desingularization discussed here, have been implemented in MAPLE.
