| Introduction |
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1 | (8) |
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9 | (18) |
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9 | (7) |
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1.2 Classification of indefinite unimodular lattices |
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16 | (4) |
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1.3 Embeddings of lattices |
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20 | (7) |
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2 Reflection groups and their fundamental domains |
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27 | (8) |
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2.1 Reflection groups and fundamental domains |
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27 | (5) |
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2.2 Reflection groups associated with lattices |
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32 | (3) |
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3 Complex analytic surfaces |
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35 | (20) |
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3.1 Basics of complex analytic surfaces |
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35 | (6) |
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3.2 Classification of complex analytic surfaces |
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41 | (3) |
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3.3 Elliptic surfaces and their singular fibers |
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44 | (11) |
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4 K3 surfaces and examples |
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55 | (20) |
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4.1 Definition and examples of K3 surfaces |
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55 | (5) |
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4.2 Reflection group associated with non-singular rational curves and the Kahler cone |
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60 | (2) |
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62 | (3) |
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4.4 The Kummer surface associated with a curve of genus 2 |
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65 | (3) |
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4.5 Torelli theorem for 2-dimensional complex tori |
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68 | (7) |
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5 Bounded symmetric domains of type IV and deformations of complex structures |
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75 | (12) |
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5.1 Bounded symmetric domains of type IV |
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75 | (5) |
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5.2 Deformations of complex structures and the Kodaira-Spencer map |
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80 | (7) |
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6 The Torelli-type theorem for K3 surfaces |
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87 | (32) |
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6.1 Periods of A3 surfaces and the Torelli-type theorem |
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87 | (4) |
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6.2 Local isomorphism of the period map (local Torelli theorem) |
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91 | (3) |
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6.3 The Torelli-type theorem for Kummer surfaces |
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94 | (9) |
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6.4 Density of the periods of Kummer surfaces |
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103 | (6) |
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6.5 Behavior of the Kahler cones under a deformation |
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109 | (3) |
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6.6 Proof of the Torelli-type theorem for K3 surfaces |
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112 | (7) |
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7 Surjectivity of the period map of K3 surfaces |
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119 | (8) |
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7.1 The period map of marked Kahler K3 surfaces |
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119 | (1) |
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7.2 Surjectivity of the period map of K3 surfaces |
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120 | (2) |
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7.3 Outline of a proof of the surjectivity of the period map of projective K3 surfaces |
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122 | (5) |
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8 Application of the Torelli-type theorem to automorphisms |
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127 | (10) |
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8.1 Automorphism group of a projective K3 surface |
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127 | (1) |
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8.2 Action of the automorphism group on the transcendental lattice |
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128 | (5) |
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8.3 A finite group that can be realized as an automorphism group of a A3 surface |
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133 | (1) |
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8.4 Automorphisms of K3 surfaces of order 2 |
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134 | (3) |
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137 | (34) |
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9.1 Periods of Enriques surfaces |
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137 | (10) |
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9.2 Non-singular rational curves and elliptic curves on Enriques surfaces |
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147 | (5) |
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9.3 Automorphism groups of Enriques surfaces |
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152 | (3) |
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9.4 Examples of Enriques surfaces |
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155 | (16) |
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10 Application to the moduli space of plane quartic curves |
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171 | (20) |
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10.1 Plane quartics and del Pezzo surfaces of degree 2 |
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171 | (9) |
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10.2 K3 surfaces associated with plane quartics |
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180 | (4) |
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10.3 The moduli space of plane quartics and a complex ball |
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184 | (7) |
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11 Finite groups of symplectic automorphisms of K3 surfaces and the Mathieu group |
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191 | (10) |
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11.1 Niemeier lattices and the Mathieu group |
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191 | (4) |
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11.2 Finite symplectic automorphisms and the Mathieu group |
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195 | (6) |
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12 Automorphism group of the Kummer surface associated with a curve of genus 2 |
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201 | (22) |
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12.1 The Leech lattice and the even unimodular lattice of signature (1, 25) |
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201 | (3) |
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12.2 Neron-Severi lattice of the Kummer surface |
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204 | (3) |
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12.3 Classical automorphisms of the Kummer surface |
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207 | (2) |
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12.4 The Kummer surface and the Leech roots |
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209 | (6) |
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12.5 Automorphism group of a generic Kummer surface |
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215 | (8) |
| Bibliography |
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223 | (8) |
| Index |
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231 | |
