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Birational geometry of algebraic varieties

Author: Kollár, János ; Mori, Shigefumi Series: Cambridge tracts in mathematics ; 134 Publisher: Cambridge University Press (CUP) 2008.Language: EnglishDescription: 254 p. ; 23 cm.ISBN: 9780521060226Type of document: BookBibliography/Index: Includes bibliographical references and index
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Item type Current location Collection Call number Status Date due Barcode Item holds
Book Europe Campus
Main Collection
Print QA155 .K65 2008
(Browse shelf)
001194822
Available 001194822
Total holds: 0

Includes bibliographical references and index

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Birational Geometry of Algebraic Varieties Contents Preface Introduction 1 Rational Curves and the Canonical Class 1.1 Finding Rational Curves when Kx is Negative 1.2 Finding Rational Curves when Kx is not Nef 1.3 The Cone of Curves of Smooth Varieties 1.4 Minimal Models of Surfaces 1.5 Ampleness Criteria 2 Introduction to the Minimal Model Program 2.1 Introduction to Mori's Program 2.2 Extensions of the Minimal Model Program 2.3 Singularities in the Minimal Model Program 2.4 The Kodaira Vanishing Theorem 2.5 Generalizations of the Kodaira Vanishing Theorem 3 Cone Theorems 3.1 Introduction to the Proof of the Cone Theorem 3.2 Basepoint-free Theorem 3.3 The Cone Theorem 3.4 The Rationality Theorem 3.5 The Non-vanishing Theorem 3.6 Relative versions 3.7 Running the MMP 3.8 Minimal and Canonical Models 4 Surface Singularities of the Minimal Model Program 4.1 Log Canonical Surface Singularities page vii 1 7 8 16 18 26 29 36 37 45 50 62 67 74 75 78 81 86 91 93 96 106 111 112 4.2 Du Val Singularities 4.3 Simultaneous Resolution for Du Val Singularities 4.4 Elliptic Surface Singularities 4.5 Deformations of Hypersurface Singularities 5 Singularities of the Minimal Model Program 5.1 Rational Singularities 5.2 Log Terminal Singularities 5.3 Canonical and Terminal Threefold Singularities 5.4 Inversion of Adjunction 5.5 Duality Theory 6 Three-dimensional Flops 6.1 Flips and Flops 6.2 Terminal Flops 6.3 Terminalization and Q-factorialization 6.4 Canonical Flops 7 Semi-stable Minimal Models 7.1 Semi-stable MMP 7.2 Semi-stable Reduction Theorem 7.3 Special Semi-stable Flips 7.4 Semi-stable Flips 7.5 Applications to Families of Surfaces 7.6 A Survey of Further Results Bibliography Index 122 128 136 144 152 153 158 164 172 179 187 188 192 195 201 207 208 214 220 224 229 236 241 249

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