| Preface to the Second Edition |
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vii | |
| Preface |
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ix | |
| Notation |
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xi | |
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1 | (4) |
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Real Projective Space, The ``Unifier'' |
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5 | (2) |
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Complex Projective Space, The Great ``Unifier'' |
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7 | (2) |
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Linear Families of Conics |
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9 | (2) |
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11 | (2) |
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13 | (4) |
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Cayley's Way of Doing Geometries of Constant Curvature |
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17 | (3) |
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Through the Looking Glass |
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20 | (2) |
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22 | (4) |
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Perpendiculars in Hyperbolic Space |
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26 | (4) |
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Circles in the K-Geometry |
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30 | (3) |
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Rational Points on Conics |
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33 | (4) |
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37 | (2) |
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39 | (3) |
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Cubics as Topological Groups |
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42 | (3) |
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The Group of Rational Points on a Cubic |
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45 | (5) |
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A Thought about Complex Conjugation |
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50 | (1) |
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Some Meromorphic Functions on Cubics |
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51 | (1) |
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Cross Ratio Revisited, A Moduli Space for Cubics |
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52 | (1) |
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The Abelian Differential on a Cubic |
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53 | (2) |
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55 | (3) |
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The Picard-Fuchs Equation |
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58 | (4) |
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Rational Points on Cubics over Fp |
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62 | (3) |
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Manin's Result: The Unity of Mathematics |
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65 | (4) |
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Some Remarks on Serre Dulity |
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69 | (4) |
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Back to the Group Law on Cubics |
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73 | (2) |
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You Can't Parametrize a Smooth Cubic Algebraically |
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75 | (3) |
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Meromorphic Functions on Elliptic Curves |
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78 | (4) |
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Meromorphic Functions on Plan Cubics |
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82 | (3) |
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The Weierstrass p-Function |
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85 | (4) |
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Theta-Null Values Give Moduli of Elliptic Curves |
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89 | (3) |
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The Moduli Space of ``Level-Two Structures'' on Elliptic Curves |
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92 | (3) |
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Automorphisms of Elliptic Curves |
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95 | (1) |
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The Moduli Space of Elliptic Curves |
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96 | (2) |
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And So, By the Way, We Get Picard's Theorem |
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98 | (2) |
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The Complex Structure of M |
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100 | (2) |
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The j-Invariant of an Elliptic Curve |
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102 | (4) |
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Theta-Nulls as Modular Forms |
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106 | (3) |
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A Fundamental Domain for Γ2 |
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109 | (2) |
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111 | (2) |
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Cohomology of a Complex Curve |
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113 | (3) |
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116 | (2) |
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The Chern Class of a Holomorphic Line Bundle |
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118 | (4) |
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Abel's Theorem for Curves |
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122 | (5) |
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The Classical Version of Abel's Theorem |
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127 | (4) |
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The Jacobi Inversion Theorem |
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131 | (1) |
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132 | (2) |
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134 | (2) |
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136 | (2) |
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Linear Systems of Degree g |
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138 | (1) |
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139 | (3) |
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Riemann's Singularities Theorem |
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142 | (5) |
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Topology of Plane Quartics |
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147 | (3) |
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The Twenty-Eight Bitangents |
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150 | (5) |
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Where Are the Hyperelliptic Curves of Genus 3? |
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155 | (3) |
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158 | (3) |
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161 | (3) |
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164 | (3) |
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Products of Pairs of Theta Functions |
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167 | (1) |
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A Proportionality Theorem Relating Jacobians and Pryms |
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168 | (5) |
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The Proportionality Theorem of Schottky-Jung |
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173 | (1) |
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174 | (7) |
| References |
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181 | (2) |
| Additional References |
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183 | (2) |
| Index |
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185 | |
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