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The Valuative Tree [[electronic resource] /] / by Charles Favre, Mattias Jonsson
| The Valuative Tree [[electronic resource] /] / by Charles Favre, Mattias Jonsson |
| Autore | Favre Charles |
| Edizione | [1st ed. 2004.] |
| Pubbl/distr/stampa | Berlin, Heidelberg : , : Springer Berlin Heidelberg : , : Imprint : Springer, , 2004 |
| Descrizione fisica | 1 online resource (XVI, 244 p.) |
| Disciplina |
510 s
511/.52 |
| Collana | Lecture Notes in Mathematics |
| Soggetto topico |
Discrete mathematics
Algebraic geometry Commutative algebra Commutative rings Topology Discrete Mathematics Algebraic Geometry Commutative Rings and Algebras |
| ISBN | 3-540-44646-X |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | 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 -- 7.2 More on the Weak Topology -- 7.3 Borel Measures -- 7.4 Functions of Bounded Variation -- 7.5 Representation Theorem I -- 7.6 Complex Tree Potentials -- 7.7 Representation Theorem II -- 7.8 Atomic Measures -- 7.9 Positive Tree Potentials -- 7.10 Weak Topologies and Compactness -- 7.11 Restrictions to Subtrees -- 7.12 Inner Products -- 8 Applications of the Tree Analysis -- 8.1 Zariski’s Theory of Complete Ideals -- 8.2 The Voûte étoilée -- A Infinitely Singular Valuations -- A.1 Characterizations -- A.2 Constructions -- B The Tangent Space at a Divisorial Valuation -- C Classification -- D Combinatorics of Plane Curve Singularities -- D.1 Zariski’s Terminology for Plane Curve Singularities -- D.2 The Eggers Tree -- E.1 Completeness -- E.2 The Residue Field -- References. |
| Record Nr. | UNISA-996466485303316 |
Favre Charles
|
||
| Berlin, Heidelberg : , : Springer Berlin Heidelberg : , : Imprint : Springer, , 2004 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. di Salerno | ||
| ||
The Valuative Tree / / by Charles Favre, Mattias Jonsson
| The Valuative Tree / / by Charles Favre, Mattias Jonsson |
| Autore | Favre Charles |
| Edizione | [1st ed. 2004.] |
| Pubbl/distr/stampa | Berlin, Heidelberg : , : Springer Berlin Heidelberg : , : Imprint : Springer, , 2004 |
| Descrizione fisica | 1 online resource (XVI, 244 p.) |
| Disciplina |
510 s
511/.52 |
| Collana | Lecture Notes in Mathematics |
| Soggetto topico |
Discrete mathematics
Geometry, Algebraic Commutative algebra Commutative rings Topology Discrete Mathematics Algebraic Geometry Commutative Rings and Algebras |
| ISBN | 3-540-44646-X |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | 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 -- 7.2 More on the Weak Topology -- 7.3 Borel Measures -- 7.4 Functions of Bounded Variation -- 7.5 Representation Theorem I -- 7.6 Complex Tree Potentials -- 7.7 Representation Theorem II -- 7.8 Atomic Measures -- 7.9 Positive Tree Potentials -- 7.10 Weak Topologies and Compactness -- 7.11 Restrictions to Subtrees -- 7.12 Inner Products -- 8 Applications of the Tree Analysis -- 8.1 Zariski’s Theory of Complete Ideals -- 8.2 The Voûte étoilée -- A Infinitely Singular Valuations -- A.1 Characterizations -- A.2 Constructions -- B The Tangent Space at a Divisorial Valuation -- C Classification -- D Combinatorics of Plane Curve Singularities -- D.1 Zariski’s Terminology for Plane Curve Singularities -- D.2 The Eggers Tree -- E.1 Completeness -- E.2 The Residue Field -- References. |
| Record Nr. | UNINA-9910144617203321 |
|
Favre Charles
|
||
| Berlin, Heidelberg : , : Springer Berlin Heidelberg : , : Imprint : Springer, , 2004 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||