The Valuative Tree
This volume is devoted to a beautiful object, called the valuative tree and designed as a powerful tool for the study of singularities in two complex dimensions. Its intricate yet manageable structure can be analyzed by both algebraic and geometric means. Many types of singularities, including those...
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| Hauptverfasser: | , |
|---|---|
| Format: | Livre numérique |
| Sprache: | Anglais |
| Veröffentlicht: |
Berlin [etc.] :
Springer
[20..].
Cham : Springer Nature |
| Schriftenreihe: | Lecture notes in mathematics
1853 |
| Schlagworte: | |
| Online Zugang: | Accès sur la plateforme de l'éditeur Accès sur la plateforme Istex Accès Université d'Orléans Accès INSA CVL |
| Anmerkung: |
Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) |
| Autres localisations: | Voir dans le Sudoc |
| Edition sous un autre format: | • The valuative tree, Charles Favre, 2004, Berlin, Springer, 1 vol. (X-234 p.), Lecture notes in mathematics, 3-540-22984-1 • The Valuative Tree, Texte imprimé, 9783662174074 |
Inhaltsangabe:
- 1 Generalities
- 1.1 Setup
- 1.2 Valuations
- 1.3 Krull Valuations
- 1.4 Plane Curves
- 1.5 Examples of Valuations
- 1.6 Valuations Versus Krull Valuations
- 1.7 Sequences of Blowups and Krull Valuations
- 2 MacLane s Method
- 2.1 Sequences of Key Polynomials
- 2.2 Classification
- 2.3 Graded Rings and Numerical Invariants
- 2.4 From Valuations to SKP s
- 2.5 A Computation
- 3 Tree Structures
- 3.1 Trees
- 3.2 Nonmetric Tree Structure on V
- 3.3 Parameterization of V by Skewness
- 3.4 Multiplicities
- 3.5 Approximating Sequences
- 3.6 Thinness
- 3.7 Value Semigroups and Approximating Sequences
- 3.8 Balls of Curves
- 3.9 The Relative Tree Structure
- 4 Valuations Through Puiseux Series
- 4.1 Puiseux Series and Valuations
- 4.2 Tree Structure
- 4.3 Galois Action
- 4.4 A Tale of Two Trees
- 4.5 The Berkovich Projective Line
- 4.6 The Bruhat-Tits Metric
- 4.7 Dictionary
- 5 Topologies
- 5.1 The Weak Topology
- 5.2 The Strong Topology on V
- 5.3 The Strong Topology on Vqm
- 5.4 Thin Topologies
- 5.5 The Zariski Topology
- 5.6 The Hausdorff-Zariski Topology
- 5.7 Comparison of Topologies
- 6 The Universal Dual Graph
- 6.1 Nonmetric Tree Structure
- 6.2 Infinitely Near Points
- 6.3 Parameterization and Multiplicity
- 6.4 The Isomorphism
- 6.5 Proof of the Isomorphism
- 6.6 Applications
- 6.7 The Dual Graph of the Minimal Desingularization
- 6.8 The Relative Tree Structure
- 7 Tree Measures
- 7.1 Outline