(Ebook PDF) Complex Algebraic Threefolds 1st edition by Masayuki Kawakita ISBN 9781108946032 1108946038 full chapters

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Product details:

ISBN 10: 1108946038
ISBN 13: 9781108946032
Author:  Masayuki Kawakita

Table of contents:

1 The Minimal Model Program

• 1.1 Preliminaries
• 1.2 Numerical Geometry
• 1.3 The Program
• 1.4 Logarithmic and Relative Extensions
• 1.5 Existence of Flips
• 1.6 Termination of Flips
• 1.7 Abundance

2 Singularities

• 2.1 Analytic Germs
• 2.2 Quotients and Coverings
• 2.3 Terminal Singularities of Index One
• 2.4 Terminal Singularities of Higher Index
• 2.5 Singular Riemann–Roch Formula
• 2.6 Canonical Singularities

3 Divisorial Contractions to Points

• 3.1 Identification of the Divisor
• 3.2 Numerical Classification
• 3.3 General Elephants for Exceptional Type
• 3.4 General Elephants for Ordinary Type
• 3.5 Geometric Classification
• 3.6 Examples

4 Divisorial Contractions to Curves

• 4.1 Contractions from Gorenstein Threefolds
• 4.2 Contractions to Smooth Curves
• 4.3 Contractions to Singular Curves
• 4.4 Construction by a One-Parameter Deformation

5 Flips

• 5.1 Strategy and Flops
• 5.2 Numerical Invariants
• 5.3 Planarity of Covering Curves
• 5.4 Deformations of an Extremal Neighbourhood
• 5.5 General Elephants
• 5.6 Examples

6 The Sarkisov Category

• 6.1 Links of Mori Fibre Spaces
• 6.2 The Sarkisov Program
• 6.3 Rationality and Birational Rigidity
• 6.4 Pliability

7 Conical Fibrations

• 7.1 Standard Conic Bundles
• 7.2 Q-Conic Bundles
• 7.3 Classification
• 7.4 Rationality
• 7.5 Birational Rigidity

8 Del Pezzo Fibrations

• 8.1 Standard Models
• 8.2 Simple Models and Multiple Fibres
• 8.3 Rationality
• 8.4 Birational Rigidity

9 Fano Threefolds

• 9.1 Boundedness
• 9.2 General Elephants
• 9.3 Classification in Special Cases
• 9.4 Classification of Principal Series
• 9.5 Birational Rigidity and K-Stability

10 Minimal Models

• 10.1 Non-Vanishing
• 10.2 Abundance
• 10.3 Birational Minimal Models
• 10.4 Nef and Mobile Cones
• 10.5 Pluricanonical Maps

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