Monomialization of Morphisms from 3-Folds to Surfaces

• Κύριος συγγραφέας: Cutkosky, Steven D. (Συγγραφέας, http://id.loc.gov/vocabulary/relators/aut)
• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2002.
• Έκδοση: 1st ed. 2002.
• Σειρά: Lecture Notes in Mathematics, 1786
• Θέματα: Algebraic geometry.; Algebraic Geometry.

A morphism of algebraic varieties (over a field characteristic 0) is monomial if it can locally be represented in e'tale neighborhoods by a pure monomial mappings. The book gives proof that a dominant morphism from a nonsingular 3-fold X to a surface S can be monomialized by performing sequence...

Πίνακας περιεχομένων:

• 1. Introduction
• 2. Local Monomialization
• 3. Monomialization of Morphisms in Low Dimensions
• 4. An Overview of the Proof of Monomialization of Morphisms from 3 Folds to Surfaces
• 5. Notations
• 6. The Invariant v
• 7. The Invariant v under Quadratic Transforms
• 8. Permissible Monoidal Transforms Centered at Curves
• 9. Power Series in 2 Variables
• 10. Ar(X)
• 11.Reduction of v in a Special Case
• 12. Reduction of v in a Second Special Case
• 13. Resolution 1
• 14. Resolution 2
• 15. Resolution 3
• 16. Resolution 4
• 17. Proof of the main Theorem
• 18. Monomialization
• 19. Toroidalization
• 20. Glossary of Notations and definitions
• References.