Introduction from a Physicist's Viewpoint |
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1 | (6) |
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7 | (10) |
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7 | (2) |
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9 | (4) |
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The Classification Problem |
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13 | (4) |
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Hints for Further Reading |
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14 | (3) |
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Topology of Riemann Surfaces |
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17 | (14) |
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17 | (4) |
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21 | (7) |
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28 | (3) |
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Hints for Further Reading |
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29 | (2) |
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31 | (12) |
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Holomorphic and Meromorphic Functions |
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31 | (4) |
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Divisors and the Theorem of Riemann--Roch |
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35 | (3) |
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Meromorphic Functions on the Torus |
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38 | (5) |
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Hints for Further Reading |
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41 | (2) |
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Differentials and Integration |
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43 | (10) |
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Tangent Space and Differentials |
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43 | (5) |
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Differential Forms of Second Order |
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48 | (2) |
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50 | (3) |
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Hints for Further Reading |
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52 | (1) |
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53 | (8) |
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53 | (2) |
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55 | (6) |
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Hints for Further Reading |
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59 | (2) |
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61 | (10) |
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61 | (4) |
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Embedding of One-Dimensional Tori |
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65 | (2) |
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67 | (4) |
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Hints for Further Reading |
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69 | (2) |
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71 | (16) |
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71 | (3) |
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74 | (4) |
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The Geometry of the Moduli Space and Its Compactification |
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78 | (9) |
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Hints for Further Reading |
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85 | (2) |
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Vector Bundles, Sheaves and Cohomology |
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87 | (16) |
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87 | (4) |
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91 | (4) |
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95 | (8) |
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Hints for Further Reading |
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100 | (3) |
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The Theorem of Riemann--Roch for Line Bundles |
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103 | (16) |
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Divisors and Line Bundles |
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103 | (6) |
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An Application: The Krichever--Novikov Algebra |
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109 | (10) |
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Hints for Further Reading |
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117 | (2) |
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The Mumford Isomorphism on the Moduli Space |
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119 | (14) |
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119 | (6) |
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The Grothendieck--Riemann--Roch Theorem |
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125 | (8) |
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Hints for Further Reading |
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131 | (2) |
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Modern Algebraic Geometry |
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133 | (22) |
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133 | (6) |
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139 | (7) |
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146 | (3) |
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149 | (6) |
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Hints for Further Reading |
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153 | (2) |
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155 | (14) |
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155 | (4) |
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159 | (3) |
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162 | (2) |
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164 | (5) |
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Hints for Further Reading |
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167 | (2) |
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Hodge Decomposition and Kahler Manifold |
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169 | (14) |
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Some Introductory Remarks on Mirror Symmetry |
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169 | (2) |
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Compact Complex Manifolds and Hodge Decomposition |
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171 | (6) |
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177 | (4) |
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Hodge Numbers of the Projective Space |
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181 | (2) |
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Hints for Further Reading |
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182 | (1) |
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Calabi-Yau Manifolds and Mirror Symmetry |
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183 | (20) |
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183 | (4) |
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K3 Surfaces, Hypersurfaces and Complete Intersections |
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187 | (5) |
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Geometric Mirror Symmetry |
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192 | (4) |
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Example of a Calabi-Yau Three-fold and Its Mirror: Results of Givental |
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196 | (7) |
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Hints for Further Reading |
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200 | (3) |
Appendix p-adic Numbers |
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203 | (10) |
Index |
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213 | |