| Titre : | Resolution of singularities of embedded algebraic surfaces |
| Auteurs : | Shreeram S. Abhyankar |
| Type de document : | texte imprimé |
| Mention d'édition : | 2e éd |
| Editeur : | Berlin : Springer-Verlag, 1998 |
| Collection : | Springer monographs in mathematics |
| ISBN/ISSN/EAN : | 978-3-540-63719-6 |
| Format : | 1 vol. (XII-309 p.) / ill., couv. ill. / 24 cm |
| Langues originales: | |
| Index. décimale : | 516.352 (Courbes et surfaces sur des plans projectifs et affines) |
| Catégories : | |
| Mots-clés: | Surfaces algébriques Singularités (mathématiques) |
| Résumé : |
This new edition describes the geometric part of the author's 1965 proof of desingularization of algebraic surfaces and solids in nonzero characteristic. The book also provides a self-contained introduction to birational algebraic geometry, based only on basic commutative algebra. In addition, it gives a short proof of analytic desingularization in characteristic zero for any dimension found in 1996 and based on a new avatar of an algorithmic trick employed in the original edition of the book. This new edition will inspire further progress in resolution of singularities of algebraic and arithmetical varieties which will be valuable for applications to algebraic geometry and number theory. It can can be used for a second year graduate course. |
| Note de contenu : |
Sommaire : Ch. 1. Local Theory. 1. Terminology and preliminaries. 2. Resolvers and principalizers. 3. Dominant character of a normal sequence. 4. Unramified local extensions. 5. Main resultsCh. 2. Global Theory. 6. Terminology and preliminaries. 7. Global resolvers. 8. Global principalizers. 9. Main resultsCh. 3. Some Cases of Three-Dimensional Birational Resolution. 10. Uniformization of points of small multiplicity. 11. Three-dimensional birational resolution over a ground field of characteristic zero. 12. Existence of projective models having only points of small multiplicity. 13. Three-dimensional birational resolution over an algebraically closed ground field of characteristic [actual symbol not reproducible] . 2, 3, 5 Appendix on Analytic Desingularization in Characteristic Zer. |
| Côte titre : |
S8/58506-58507 |
Exemplaires (2)
| Cote | Support | Localisation | Disponibilité |
|---|---|---|---|
| S8/58506 | Livre | Bibliothèque centrale | Disponible |
| S8/58507 | Livre | Bibliothèque centrale | Disponible |
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