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| Voisin C. — Hodge theory and complex algebraic geometry 1 |
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| Предметный указатель |
Abel — Jacobi map 290 292 294 303
Abel — Jacobi, invariant 14 15
Acyclic object 102 193
Acyclic, complex 192
Acyclic, resolution 103 105
Acyclic, resolution, flasque 106 109
Almost complex structure 44 61
Analytic, closed set 173
Analytic, complex 21 29
Analytic, continuation 31
Analytic, cycle 272 273
Analytic, cycle, class of an 273
Analytic, real 39 51 222
Analytic, subset 32 264 265
Analytic, subset, class of an 269
Analytic, subset, stratification of an 269
Blowup of a submanifold 78
Bundle, cotangent 42
Bundle, holomorphic line 81
Bundle, holomorphic vector 43
Bundle, line 75
Bundle, normal 80
Bundle, projective 77 80
Bundle, tangent 41
Bundle, vector 40
Category 95
Category of Abelian groups 95
Category of Hodge structures 175
Category of sheaves of groups over X 95 102
Category, abelian 95
Cauchy formula 21 27—30 33 34
Cech 92
Cech resolution 93
Cech, cocycle 163
Cech, cohomology 105 107 110 157 224
Cech, complex 105
Cech, differential 163
Chern class 162 276 279 280
Chern connection 71 72 75
Chern form 75 78 81 157 163—165
Chern polynomial 276
Cohomology and harmonic forms 129 137
Cohomology of a complex 99
Cohomology of sheaves 83 103
Cohomology, Cech 105 111
Cohomology, de Rham 68 105 108
Cohomology, Dolbeault 105 129 135
Cohomology, singular 108 109
Complex Cech 93
Complex conjugate 22
Complex coordinate 22
Complex differential form 27
Complex in an abelian category 96
Complex of sheaves 92
Complex of singular chains 108
Complex of singular cochains 110
Complex, de Rham 177
Complex, de Rham, holomorphic 184 196
Complex, de Rham, holomorphic logarithmic 197
Complex, Deligne 304
Complex, Dolbeault 59 94
Complex, double 106 201
Complex, double, spectral sequence of a 204
Complex, exact 99
Complex, filtered 200
Complex, hypercohomology of a 194
Complex, injective resolution of a 186
Complex, manifold 21 43 61 63
Complex, protective space 60
Complex, simple associated to a double 106
Complex, structure 23
Complex, structure, deformation of 222
Complex, structure, infinitesimal deformation of 223 226
Complex, submanifold 64 68
Complex, torus 168 292 298
Complex, vector bundle 40
Complex, vector bundle, holomorphic 43
Complex, vector space, Hermitian 64
Cone of morphism of complexes 191 192 307
Connection 69
Connection, Chern 71 72 75
Connection, flat 228—230
Connection, Gauss — Manin 231 249 251
Connection, Levi — Civita 70 72
Connection, matrix of a 70 72
Cup-product 130—133 144 148 178 240 253 255 259
Curvature 229
CURVES 59 60 254
De Rham cohomology 117 142
de Rham cohomology, class 148
de Rham, complex 163
de Rham, complex, algebraic 206
de Rham, complex, holomorphic 196 205
de Rham, complex, holomorphic logarithmic 197 208
de Rham, complex, relative 246
de Rham, resolution 93 105 161
de Rham, theorems 108
Deligne cohomology 290 304 305 308
Deligne cohomology, class of a cycle in 310
Deligne complex 304 307
Deligne theorem 210 213
Deligne — Illusie theorem 207
Differential characters 306
Differential form, complex 22
Dolbeault cohomology 85 135 226
Dolbeault complex 59
Dolbeault operator 57
Dolbeault resolution 94
Dolbeault theorem 105
Duality 130
Duality, Poincare 133 134 154 178 285 287
Duality, Serre 134 255
Ehresmann, trivialisation theorem 220
Filtration by the first index 204
Filtration by weight 210 214
Filtration by weight on the logarithmic complex 208
Filtration of an object in an abelian category 200
Filtration of the de Rham complex 204
Filtration, Hodge 184 214
Filtration, Hodge, induced on the cohomology 200
Filtration, Hodge, on a complex in an abelian category 200
Filtration, Hodge, on the cohomology of a complex manifold 185
Filtration, Hodge, on the cohomology of an open manifold 207
Filtration, Leray 208
Filtration, naive 200
Filtration, spectral sequence associated to a 202
Filtration, weight on the cohomology of an open manifold 213
Formal adjoint 121
Formal adjoint, existence 128
Forms, harmonic 124
Frobenius theorem 46 48 230
Frobenius theorem, holomorphic 51
Froelicher, spectral sequence 204 205
Froelicher, spectral sequence, degeneracy of 205—207 235 244
Fubini — Study, metric 76
Functor of global sections 96
Functor, composed 194
Functor, derived 99
Functor, derived, of a complex 184
Functor, left-exact 96
Gauss — Manin connection 228 231 240 249 251
Grassmannian 241 249 251 258
Grassmannian, compactness of 241
Grassmannian, projectivity of 242
Grassmannian, tangent space of 242
Grassmannian, tautological bundle over 242 283
Grassmannian, universality of 283
Griffiths group 302 303
Griffiths, Abel — Jacobi map 292
Griffiths, Abel — Jacobi map, properties 294
| Griffiths, period map 244
Griffiths, period map, differential 253
Griffiths, transversality 246
Gysin morphism 176 178 210—212
Harmonic forms 129
Hartogs extension theorem 33
Hartogs theorem 165
Hodge bundles 249 250
Hodge class 273 279 280
Hodge conjecture 14 284 287
Hodge decomposition 5 137 142 205
Hodge filtration 158 184 248
Hodge filtration on the cohomology of an open manifold 213
Hodge index theorem 150 152
Hodge numbers 235
Hodge operator 119
Hodge structure 156—158 176
Hodge structure, infinitesimal variation of 256 257
Hodge structure, mixed 214
Hodge structure, morphism of 174 279 286
Hodge structure, of a blowup 180
Hodge structure, of K3type 171
Hodge structure, of weight 1 168 169
Hodge structure, of weight 2 170
Hodge structure, polarised 160
Hodge structure, tensor product of 286
Hodge structure, variation of 239
Hodge symmetry 2 3 180 206
Hodge theory 5
Homotopy 97
Hopf surface 143
Injective group 102
Injective morphism in an abelian category 97
Injective morphism of sheaves 90
Injective object 96 98—100
Integrability of a distribution 48
Integrability of a holomorphic distribution 51
Integrability of an almost complex structure 50 54 59
Intersection form 152
Jacobian matrix 41
Jacobian matrix, holomorphic 46
Jacobian, intermediate 292 298 305
Kaehler class 68 161
Kaehler form 66 68 72
Kaehler identities 139
Kaehler manifolds 68
Kaehler manifolds, examples of 75 78 80
Kaehler metric 66 67
Kaehler metric, characterisation of 72
Kaehler metric, Laplacians for a 141
Kaehler metric, normal form 73
Kodaira embedding theorem 164
Kodaira vanishing theorem 164 233 283
Kodaira — Spencer map 223 226 240
Kuenneth component 287 301
Kuenneth formula 199 285
Laplacian 8 119
Laplacian, associated to the operator  137
Laplacian, commutation with the Lefschetz operator 8
Lefschetz decomposition 138 144 148 152 248
Lefschetz decomposition on forms 146
Lefschetz isomorphism 287
Lefschetz operators 144
Lefschetz theorem, hard 148
Lefschetz theorem, on (1,1) classes 156 267
Lelong formula 282
Lelong integration current 273
Leray — Hirsch theorem 181 195 271
Lie bracket 46
Local system 17 228—230 250
Metric,  117 119 121
Metric, Fubini — Study 76
Metric, Hermitian 60 64 66 124 137
Metric, Hermitian on a bundle 78 122
Metric, Hermitian on a complex bundle 70
Metric, Hermitian on a line bundle 75
Metric, Kaehler 67
Metric, Kaehler, characterisation 72
Metric, Kaehler, normal form 73
Metric, Riemannian 60 71 119
Mixed Hodge structure 214
Operator, 35 55 56
Operator,  58 59 70 94
Operator, adjoint of 123
Operator, almost complex structure 50
Operator, complex structure 45
Operator, d* 121
Operator, differential 125 128
Operator, differential adjoint 128
Operator, differential, elliptic 126 234 236
Operator, differential, symbol of a 126 140
Operator, Hodge 119
Operator, Lefschetz 139 160
Period domain 171 173 246 248 249
Period domain, polarised 248
Period map 240 243 244 254 258
Period map for curves 254
Period map, differential of the 251
periods 171 293
Picard 168
Picard group 162
Picard variety 170 296
Poincare duality 133 154 178
Poincare lemma 55 94
Presheaf 85
Primitive cohomology 149 152
Primitive form 146 147 153
Quasi-isomorphism 97 186 189—192
Rautological subbundle over a projective bundle 77
Rautological subbundle over projective space 76
Rautological subbundle over the Grassmannian 242
Residue 173 209—211
Resolution 91 97 196
Resolution, acyclic 102 103
Resolution, Cech 93
Resolution, de Rham 94 105
Resolution, de Rham, holomorphic 196
Resolution, Dolbeault 94 105
Resolution, flasque 106 176
Resolution, Godement 103
Resolution, injective 97—99 104 107 109 195
Riemann extension theorem 32
Riemann Relations 152
Riemann surfaces 59
Serre duality 135
Serre GAGA principle 206
Sheaf 85
Sheaf of A-modules 88
Sheaf, constant 87
Sheaf, fine 104
Sheaf, flasque 103
Signature 153
Singular chain 169
Singular cochain 177
Singular cohomology 108—110 167 177
Singular cohomology, relative 167
Singular form 212 282 311
Singular integral 35 36
Singular manifold 285
Spectral sequence 202 204
Spectral sequence for the weight filtration 208 210 213
Spectral sequence, degeneracy of 204
Spectral sequence, Froelicher 205
Spectral sequence, Froelicher, degeneracy of 207
Spectral sequence, Leray 208
Split exact sequence 100 192
Stokes formula 24 26 68 69 110 128 135 272
Symbol 140
Symbol of a differential operator 126
Symbol of the Laplacian 126 140
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