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Köp båda 2 för 865 kr1 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 MacLanes Method.- 2.1 Sequences of Key Polynomials.- 2.2 Classification.- 2.3 Graded Rings and Numerical Invariants.- 2.4 From Valuations to SKPs.- 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.- 8.1Zariskis Theory of Complete Ideals.- 8.2 The Vote toile.- 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 Zariskis Terminology for Plane Curve Singularities.- D.2 The Eggers Tree.- E.1 Completeness.- E.2 The Residue Field.- References.