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Table of Contents
Cover
Title page
Introduction
Chapter 1. Generalities
1.1. Cancellation and the Makar-Limanov invariant
1.2. Non-cancellation and Gizatullin surfaces
1.3. The Danielewski-Fieseler construction
1.4. Affine modifications
Chapter 2. ¹-fibered surfaces via affine modifications
2.1. Covering trick and GDF surfaces
2.2. Pseudominimal completion and extended divisor
2.3. Blowup construction
2.4. GDF surfaces via affine modifications
Chapter 3. Vector fields and natural coordinates
3.1. Locally nilpotent vertical vector fields
3.2. Standard affine charts
3.3. Natural coordinates
3.4. Special _{ }-quasi-invariants
3.5. Examples of GDF surfaces of Danielewski type
Chapter 4. Relative flexibility
4.1. Definitions and the main theorem
4.2. Transitive group actions on Veronese cones
4.3. Relatively transitive group actions on cylinders
4.4. A relative Abhyankar-Moh-Suzuki Theorem
Chapter 5. Rigidity of cylinders upon deformation of surfaces
5.1. Equivariant Asanuma modification
5.2. Rigidity of cylinders under deformations of GDF surfaces
5.3. Rigidity of cylinders under deformations of ¹-fibered surfaces
5.4. Rigidity of line bundles over affine surfaces
Chapter 6. Basic examples of Zariski factors
6.1. Line bundles over affine curves
6.2. Parabolic _{ }-surfaces: an overview
6.3. Parabolic _{ }-surfaces as Zariski factors
Chapter 7. Zariski 1-factors
7.1. Stretching and rigidity of cylinders
7.2. Non-cancellation for GDF surfaces
7.3. Extended graphs of Gizatullin surfaces
7.4. Zariski 1-factors and affine ¹-fibered surfaces
Chapter 8. Classical examples
Chapter 9. GDF surfaces with isomorphic cylinders
9.1. Preliminaries
9.2. Classification of GDF cylinders up to -isomorphism
9.3. GDF surfaces whose fiber trees are bushes.
9.4. Spring bushes versus bushes
9.5. Cylinders over Danielewski-Fieseler surfaces
9.6. Proof of the main theorem
Chapter 10. On moduli spaces of GDF surfaces
10.1. Coarse moduli spaces of GDF surfaces
10.2. The automorphism group of a GDF surface
10.3. Configuration spaces and configuration invariants
10.4. Versal deformation families of trivializing sequences
10.5. Proof of Theorem 10.1.3
Acknowledgments
Bibliography
Back Cover.
Title page
Introduction
Chapter 1. Generalities
1.1. Cancellation and the Makar-Limanov invariant
1.2. Non-cancellation and Gizatullin surfaces
1.3. The Danielewski-Fieseler construction
1.4. Affine modifications
Chapter 2. ¹-fibered surfaces via affine modifications
2.1. Covering trick and GDF surfaces
2.2. Pseudominimal completion and extended divisor
2.3. Blowup construction
2.4. GDF surfaces via affine modifications
Chapter 3. Vector fields and natural coordinates
3.1. Locally nilpotent vertical vector fields
3.2. Standard affine charts
3.3. Natural coordinates
3.4. Special _{ }-quasi-invariants
3.5. Examples of GDF surfaces of Danielewski type
Chapter 4. Relative flexibility
4.1. Definitions and the main theorem
4.2. Transitive group actions on Veronese cones
4.3. Relatively transitive group actions on cylinders
4.4. A relative Abhyankar-Moh-Suzuki Theorem
Chapter 5. Rigidity of cylinders upon deformation of surfaces
5.1. Equivariant Asanuma modification
5.2. Rigidity of cylinders under deformations of GDF surfaces
5.3. Rigidity of cylinders under deformations of ¹-fibered surfaces
5.4. Rigidity of line bundles over affine surfaces
Chapter 6. Basic examples of Zariski factors
6.1. Line bundles over affine curves
6.2. Parabolic _{ }-surfaces: an overview
6.3. Parabolic _{ }-surfaces as Zariski factors
Chapter 7. Zariski 1-factors
7.1. Stretching and rigidity of cylinders
7.2. Non-cancellation for GDF surfaces
7.3. Extended graphs of Gizatullin surfaces
7.4. Zariski 1-factors and affine ¹-fibered surfaces
Chapter 8. Classical examples
Chapter 9. GDF surfaces with isomorphic cylinders
9.1. Preliminaries
9.2. Classification of GDF cylinders up to -isomorphism
9.3. GDF surfaces whose fiber trees are bushes.
9.4. Spring bushes versus bushes
9.5. Cylinders over Danielewski-Fieseler surfaces
9.6. Proof of the main theorem
Chapter 10. On moduli spaces of GDF surfaces
10.1. Coarse moduli spaces of GDF surfaces
10.2. The automorphism group of a GDF surface
10.3. Configuration spaces and configuration invariants
10.4. Versal deformation families of trivializing sequences
10.5. Proof of Theorem 10.1.3
Acknowledgments
Bibliography
Back Cover.