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| Ueno K. — Advances in Moduli Theory |
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| Предметный указатель |
 orbit 165
orbit theorem 165
 -polarized abelian variety 49
Abel — Jacobi mapping 107
Abelian category 112
Abelian variety 41
Abel’s theorem 61
Adjoint representation 32
Affine Grassmannian 274
Albanese variety 60
Algebraic curve 182
Algebraic stack (in the sense of Artin) 273
Analytic family 2
Analytic family of G-bundles 31
Analytic family of G-bundles, parametrized by S 31
Appell — Humbert Theorem 42
Bidifferential 243
Calabi — Yau variety 140
Canonical curve 73
Canonical extension 163
Canonical mapping 76
Canonical prolongation 120 163
Cartan — Killing form, normalized 193
Central charge 198
Classifying space of Hodge structures 124
Clebsch — Gordan coefficient 267
Clemens — Schmid exact sequence 169
Coarse moduli space 93
Cohomological mixed Hodge complex 159
complete 8
Complex analytic family 2
Complex analytic family of G-bundles 31
Complex torus 36
Conformal blocks 207
Conformal blocks, dual 207
Conformal blocks, sheaf of 234
Conformal blocks, sheaf of dual 234
Connected sum 214
Connection flat 115
Connection, Gauss — Manin 117
Connection, integrable 115
Connection, projective 244
Contraction 135
Correlation function 223
Correlation function of currents 225
Correlation function of energy-momentum tensors 225
Critical locus 189
Current 197
Deformation 2
Deformation of a principal G-bundle 31
Discriminant locus 189
Divisor with normal crossings 155
Dominant integral weight 195
Donagi’s theorem 146
Dual conformal block 207
Dualizing sheaf 183
Effective divisor 61
Energy-momentum tensor 197
Factorization theorem 230
Faltings’ theorem 269
Family of stable N-pointed curves of genus g with formal neighbourhoods 186
Family of stable N-ppointed curves of genus g with n-th infinitesimal neighbourhoods 187
Filtered R-module 209
Filtered ring 208
Filtration N- 166
Filtration, Hodge 108
Filtration, limit Hodge 164
Filtration, monodromy weight 166
Filtration, stupid 157
Filtration, weight 150
Flat connection 96
Formal coordinates 185
Formal neighbourhoods 184
Fusion ring (or fusion algebra) 264
Fusion rule 264
Fusion rule, non-degenerate 264
Gabber’s theorem 209
Gauge condition 208
Gauss map 78
Gauss — Manin connection 117
Gauss — Manin connection, regularity of 120
Generic global Torelli problem 137
Genus 182
Graded ring 208
Graded-polarizable 151
Griffiths transversality 118
Hard Lefschetz theorem 110
Highest weight 195
Highest weight vector 111 195
Hironaka’s theorem on resolution of singularities 155
Hirzebruch — Nagata surface 13
Hodge decomposition 103
Hodge filtration 108
Hodge index theorem 115
Hodge structure of Tate type 105
Hodge structure, A-Hodge structure 104
Hodge structure, classifying space of 124
Hodge structure, morphism of A-Hodge structure 112
Hodge structure, polarization 113 121
Hodge structure, Tate Hodge structure 105
Hodge structure, variation of A-Hodge structure 118
Hodge — Riemann bilinear relations 114
Hopf surface 14
Horizontal map 134
Horizontal tangent bundle 133
Horizontal tangent vector space 129 133
Hyperelliptic involution 82
Index of unipotency 162
Infinitesimal deformation 4
Infinitesimal Torelli problem 136 138
Infinitesimal variation of Hodge structure 146
Integrable highest weight representations 195
Integrable symplectic group 46
Intermediate Jacobian variety 106
Isogeny 71
Jacobian variety 60
Kaehler differential 183
Kaehler morphism 115
Knizhnik — Zamolodchikov equation 259
Kodaira — Spencer mapping 5
Kuranishi family 10
| Kuranishi space 10
KZ equation 259
Label 207
Lefschetz operator 110
Level 195
Level n-structure 51
Limit Hodge filtration 164
Limit mixed Hodge structure 165
Local invariant cycle theorem 170
Locally liftable map 134
Locally nilpotent 196
Logarithmic differential form 156
Loop Grassmannian 274
Mixed Hodge structure (MHS) 150
Mixed Hodge structure limit 165
Mixed Hodge structure, graded-polarizable 151
Mixed Hodge structure, morphism of 151
Mixed Hodge structure, pure 151
Moderate growth, 120
Monodromy representation 131
Monodromy theorem 162
Monodromy weight filtration 166
Morphism of A-Hodge structure 112
Morphism of mixed A-Hodge structures 151
N-filtration 166
N-th infinitesimal neighbourhoods 184
Nagata’s embedding theorem 155
Newlander — Nirenberg theorem 29
Nilpotent orbit 164
Nilpotent orbit theorem 164
Normal ordering 196
Normalized Cartan — Killing form 193
Obstruction class 21
Orbit 165
Orbit, nilpotent 164
Ordinary double point 182
Paramodular group 46
Perfect pairing 203
Period domain 124
Period domain, compact dual 124
Period mapping 132
Period matrix 36 56
Picard variety 39
Picard — Puchs equation 97
Poincare residue 156
Poisson bracket 209
Polarization 113 121
Polarization of type  49
Polarization of type 49
Polarized Abelian variety 49
Polarized abelian variety of type 49
Primitive decomposition 111
Primitive part 110
Principal G-bundle 31
Principally polarized abelian variety 49
Projective connection 244
Prym mapping 148
Prym variety 148
Pullback family 2
Pure mixed Hodge structure 151
Quasi-isomorphic 108
Quasi-unipotent 162
Regularity of Gauss — Manin connection 120
Removable singularity theorem 135
Riemann conditions 45 59
Riemann constant 65
Riemann theta function 53
Root vector 193
Satake compactification 52
Schottky problem 96
Schwarzian derivative 217
Semi-character 42
Semi-stable curve 182
Semi-stable degeneration 161
Semi-stable reduction theorem 161
Semi-universal 9
Sheaf of conformal blocks 234
Sheaf of dual conformal blocks 234
Siegel modular group 46
Siegel upper half plane 46
Siegel upper half space 46
Smooth 10
Smooth family 2
Spectral sequence, Hodge-to-de Rham 107
Spectral sequence, Leray 159
Spectral sequence, weight 157
Stable N-pointed curve 182
Stable N-pointed curve with formal neighbourhoods 184
Stable N-pointed curve with n-th infinitesimal neighbourhoods 184
Strictly compatible 112
Stupid filtration 157
Symmetric product 62
Symplectic basis 45
Tate twist 105
Theorem of the fixed part 160
Theta characteristic 54
Theta divisor 63
Theta function, Riemann 53
Torelli 136
Torelli, generic global Torelli problem 137
Torelli, global Torelli problem 137
Torelli, infinitesimal Torelli problem 136 138
Torelli, local Torelli problem 138
Torelli, Torelli’s theorem 78
Torelli, weak global Torelli problem 137
Unipotent 162
Universal 9
Vacua 207
Variation of (A-)Hodge structure (VHS) 118
Variation of (A-)Hodge structure (VHS), infinitesimal 146
Variation of (A-)Hodge structure (VHS), morphism of 121
Variation of (A-)Hodge structure (VHS), polarized 121
Varieties with normal crossings 160
Verlinde formula 261 262
Verlinde isomorphism 271
Versal 9
Virasoro algebra 198
Weak global Torelli problem 137
Weight filtration 150
Weil operator 113
Zariski tangent space 10
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