Book Volume 181 2000

Resolution of Singularities

A research textbook in tribute to Oscar Zariski Based on the courses given at the Working Week in Obergurgl, Austria, September 7–14, 1997

Editors:

ISBN: 978-3-0348-9550-7 (Print) 978-3-0348-8399-3 (Online)

Table of contents (21 chapters)

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  1. Front Matter

    Pages i-xxi

  2. Oscar Zariski 1899–1986

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      Chapter

      Pages 1-4

      Oscar Zariski 1899–1986

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      Chapter

      Pages 5-36

      Resolution of Singularities 1860–1999

  3. Classes of the Working Week

    1. Front Matter

      Pages 37-37

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      Chapter

      Pages 39-108

      Alterations and Resolution of Singularities

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      Chapter

      Pages 109-128

      Reduction of Singularities for Differential Equations

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      Chapter

      Pages 129-145

      Puiseux Solutions of Singular Differential Equations

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      Chapter

      Pages 147-227

      A Course on Constructive Desingularization and Equivariance

  4. Contributions

    1. Front Matter

      Pages 229-229

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      Chapter

      Pages 231-238

      A Computer Program for the Resolution of Singularities

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      Chapter

      Pages 239-258

      Uniformisation et désingularisation des surfaces d’après Zariski

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      Chapter

      Pages 259-284

      Toric Varieties and Toric Resolutions

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      Chapter

      Pages 285-298

      A Compactification of a Fine Moduli Space of Curves

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      Chapter

      Pages 299-314

      Applications of de Jong’s Theorem on Alterations

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      Chapter

      Pages 315-340

      Resolving Singularities of Plane Analytic Branches with one Toric Morphism

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      Chapter

      Pages 341-373

      Excellent Surfaces and Their Taut Resolution

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      Chapter

      Pages 375-380

      An Application of Alterations to Dieudonné Modules

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      Chapter

      Pages 381-456

      Valuation Theoretic and Model Theoretic Aspects of Local Uniformization

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      Chapter

      Pages 457-483

      Les Singularités Sandwich

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      Chapter

      Pages 485-505

      Equisingularity and Simultaneous Resolution of Singularities

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      Chapter

      Pages 507-517

      Resolution of Weighted Homogeneous Surface Singularities

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      Chapter

      Pages 519-532

      Alterations and Birational Anabelian Geometry

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      Chapter

      Pages 533-537

      The Turbulent Fifties in Resolution of Singularities

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