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INICIO | 29 de marzo de 2024
  

A simplified proof of desingularization and applications.

Título inglés A simplified proof of desingularization and applications.
Título español Una demostración simplificada de la desingularización y aplicaciones.
Autor/es Bravo, Ana María ; Encinas, Santiago ; Villamayor Uriburu, Orlando
Organización Dep. Mat. Fac. Cienc. Univ. Autón. Madrid, Cantoblanco (Madrid), España;Dep. Mat. Apl. Esc. Téc. Super. Ing. Arquit. Univ. Valladolid, Valladolid, España
Revista 0213-2230
Publicación 2005, 21 (2): 349-458, 36 Ref.
Tipo de documento articulo
Idioma Inglés
Resumen inglés This paper contains a short and simplified proof of desingularization over fields of characteristic zero, together with various applications to other problems in algebraic geometry (among others, the study of the behavior of desingularization of families of embedded schemes, and a formulation of desingularization which is stronger than Hironaka's). Our proof avoids the use of the Hilbert-Samuel function and Hironaka's notion of normal flatness: First we define a procedure for principalization of ideals (i.e. a procedure to make an ideal invertible), and then we show that desingularization of a closed subscheme X is achieved by using the procedure of principalization for the ideal I(X) associated to the embedded scheme X. The paper intends to be an introduction to the subject, focused on the motivation of ideas used in this new approach, and particularly on applications, some of which do not follow from Hironaka's proof.
Clasificación UNESCO 120101
Palabras clave español Geometría algebraica ; Singularidades ; Geometría birracional
Código MathReviews MR2174912
Código Z-Math Zbl 1086.14012
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Equipo DML-E
Instituto de Ciencias Matemáticas (ICMAT - CSIC)
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