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| Voisin C. — Hodge theory and complex algebraic geometry 2 |
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| Предметный указатель |
Abelian variety 328
Abelian variety, dual 336
Affine variety 28
Affine variety, homotopy type of a 30 34
Affine variety, index of the square of the distance function on a 29
Affine variety, Morse theory on 28
Bloch — Beilinson conjectures 14
Bloch — Chow groups of abelian varieties 332
Bloch — Srinivas construction 291
Bloch, conjecture 308 322
Bloch, conjecture, for Godeaux surfaces 315
Bloch, conjecture, for surfaces of Kodaira dimension 313
Bloch, filtration on  329
Castelnuovo criterion 311
Castelnuovo theorem 311 315
Chow groups 12 236 247
Chow groups, filtration on 322
Chow groups, of abelian varieties 329
Chow groups, of blowups 271
Chow groups, of hypersurfaces 273
Chow groups, of projective bundles 269
Complex torus 4 153 190
Correspondences 246 259
Correspondences, action of 259
Correspondences, compatibility with cycle class maps 264
Correspondences, composition of 260
Correspondences, stability under 307 324
Critical point 20
Critical point, degenerate, of the square of the distance function 28
Critical point, index of the square of the distance function 29
Critical point, isolated 21
Critical point, Morse index of 21
Critical point, non-degenerate 20 21
Critical point, of a holomorphic function 47
Critical value 20 27
Critical value, monodromy around a 81
Critical value, of a Lefschetz pencil 42
Critical value, of a pencil 235
Cycles, algebraic 228 247
Cycles, algebraically equivalent to 0 237
Cycles, classes of 261
Cycles, intersection of 256
Cycles, invariant 75 118 124
Cycles, rationally equivalent to 0 247
Cycles, vanishing 60 87—89 210
de Rham algebraic complex 10
de Rham cohomology class 160 168
de Rham complex 109 132
de Rham complex, holomorphic 132 137 219
de Rham complex, logarithmic 158 161 162 221
de Rham complex, of a flat bundle 110 111 130 131
de Rham filtration on the holomorphic de Rham complex 137
de Rham resolution 132
Decomposition, generalised Hodge 120
Decomposition, Hodge 120
Decomposition, of the diagonal 292 301
Deligne cohomology 266
Deligne complexes 267
Deligne degeneration theorem 117
Deligne invariant cycles theorem 124
Deligne mixed Hodge structure on the relative cohomology 220
Divisor, Cartier 35 90 248 251 252
Divisor, divisor class 94
Divisor, exceptional 271
Divisor, modulo rational equivalence 228
Divisor, normal crossing 221 222
Divisor, of a rational function 247
Divisor, of a section 37
Donagi generic Torelli theorem 179 180 182
Equivalence, algebraic 228 236
Equivalence, homological 228
Equivalence, rational 35 247
Exact sequence, Euler 165
Exact sequence, exponential 35 91
Exact sequence, homotopy 85
Exact sequence, localisation 254 270
Exact sequence, normal 170
Exact sequence, of relative cohomology 56 159
Exact sequence, of relative homology 61
Exceptional curve 311
Exceptional curve, exceptional divisor 271
Filtration, Bloch 332
Filtration, by the order of the pole 160
Filtration, Hodge 119 133 158 220 221
Filtration, Leray 12 118 137 139 224 231
Filtration, Nori 236
Filtration, on Chow groups 323 324
Filtration, Saito 327
Filtration, weight 119 220 221
Fourier transform 336
Function field 209
Function, exhaustion 23 27
Function, Morse 23
Function, normal 142 191
Function, normal, associated to a cycle 200
Function, normal, Hodge class of a 229
Function, normal, infinitesimal invariant of a 193
Function, normal, locally flat 208
Function, normal, torsion 209
Function, rational 247
Function, rational, divisor of a 249
Function, rational, on a curve 250
Function, square of the distance 28
Function, square of the distance, on affine varieties 28
Functoriality of the Chow groups 248
Functoriality of the cycle class map 263
Gauss — Maninconnection 111 131 136 168 208
Green density criterion 151
Green syzygies of projective space 176 226
Green triviality of the Abel-Jacobi map 207
Griffiths algebraic equivalence 229
Griffiths cycles not algebraically equivalent to 0 233
Griffiths Dolbeault cohomology of hypersurfaces 164
Griffiths filtration by the order of the pole 160
Griffiths group 229 233 238 300
Griffiths horizontality of the Abel-Jacobi map 194
Griffiths infinitesimal invariant 142 193
Griffiths IVHS of hypersurfaces 167
Griffiths transversality 134
Hodge class 144 267
Hodge class of a cycle 261
Hodge class of normal functions 230
Hodge conjecture 298
Hodge decomposition 1 37 133
Hodge loci 144
Hodge loci for hypersurfaces 178 179
Hodge structure 75
Hodge structure, mixed 123
| Hodge structure, morphisms of mixed 120
Hodge structure, variation of 134 143
Hodge substructure 75
Hodge symmetry 220
Horizontality 191 194 207 209
Index, filtration by the second 103
Index, Morse 21 27
Index, Morse, of the distance function on affine varieties 29
Index, of a quadratic form 21
Index, subgroup of finite 209
Intermediate Jacobian 190
Intersection form 7 59 74 80 88 210
Intersection, compatibility 259
Intersection, complete 35 93
Intersection, complete, locally 257 258
Intersection, complete, universal 217 239
Intersection, of cycles 256
Intersection, proper 258
Intersection, refined 256 258
Invariant cycles 118
Invariant cycles, theorem 75 124
Invariants, Abel — Jacobi 193
Invariants, birational 309
Invariants, infinitesimal 141 207
Invariants, infinitesimal, comparison of 200
Invariants, infinitesimal, of normal functions 193
Invariants, under a group 314 317
Invariants, under translation 333
Isomorphism, Lefschetz 2 4
Isomorphism, Lefschetz restriction 33
Isomorphism, of line bundles 35
Isomorphism, of local systems 71
Isomorphism, Poincare duality 33
Isomorphism, Roitman 13 284
Isomorphism, Thorn 56 159
Kunneth component 266 276 325
Kunneth decomposition 266 276
Lefschetz decomposition 2 115
Lefschetz degeneration 47
Lefschetz hard theorem 32
Lefschetz operator 57
Lefschetz pencils 42 43 45 46 54
Lefschetz pencils, cohomological study 53 58
Lefschetz pencils, monodromy 77
Lefschetz theorem on (1, l)-classes 148 319
Lefschetz theorem on hyperplane sections 31 32 217
Level sets 23
Level sets, change of topology 27
Level, Hodge 10 178
Logarithmic complex 158 161 221
Logarithmic form with singularity 161
Macaulay Theorem 171 177
Meromorphic form 160 161 163 165
Meromorphic section 248
monodromy 6 67 73 75 87 209
Monodromy, action, irreducibility 87 88
Monodromy, local 75
Monodromy, Picard — Lefschetz formula 78
Monodromy, quasiunipotence 75
Monodromy, representation 69
Morphism, Gysin 31 58 159
Morphism, of complexes 100
Morphism, of filtered complexes 105
Morphism, of Hodge structures 124
Morphism, of local systems 69 88 116
Morphism, of mixed Hodge structures 120 123
Morphism, of spectral sequences 105 106 115 116
Morphism, projective 115
Morphism, strict 119
Morphism, submersive 74
Morse function 23
Morse holomorphic lemma 46
Morse index 21
Morse lemma 20 21
Morse theory 24 26 27
Morse theory, on affine varieties 28 34
Mumford’s theorem 12 289 296
Mumford’s theorem, converse of 308
Mumford’s theorem, generalisation of 290 294
Noether — Lefschetz locus 89 92 148
Noether — Lefschetz locus, density 151
Noether — Lefschetz locus, infinitesimal study 150
Noether — Lefschetz theorem 11 93
Noether — Lefschetz theorem, generalisation 178
Noether’s formula 312 313
Nori connectivity theorem 12 217
Nori filtration 235
Nori theorem 237
Picard — Lefschetz formula 77 78 80 89
Poincare bundle 336
Poincare duality 190 196 231 235 262
Pontryagin product 328
Rational cohomology 10 37 218
Rational curve 299 309
Rational equivalence 12 228 247
Rational function 247 250
Rational Hodge class 151
Rational Hodge structure 119 124
Rational Hodge structure, variation of 143
Rational map 310
Rational section 252 294
Rational surface 311 315
Regular sequence 172 175
Representability, characterisation of 282 284
Representability, of Chow groups 281 284
Residue 159 163 166
Roitman generalisation of Mumford’s theorem 290
Roitman theorem on the representability of the group  13 284
Roitman theorem on the torsion in the group 289
Spectral sequence, degeneration of 117
Spectral sequence, Frolicher 162 194
Spectral sequence, hypercohomology 173
Spectral sequence, Leray 11 109 110 217
Spectral sequence, Leray, holomorphic 138 139 225
Spectral sequence, of a complex of acyclic objects 100
Spectral sequence, of a composed functor 107
Spectral sequence, of Ext 109
Spectral sequence, spherical 112 173
Structure, Hodge 75
Structure, mixed Hodge 119 220
Symmetriser lemma 175 179 205 206
Syzygies of projective space, vanishing of 176
Transversality 3 8 11 76 134 135 137 144 191
Vanishing of syzygies 10
Vanishing theorem of Akizuki, Kodaira and Nakano 36
Vanishing theorem of Bott 91 173
Vanishing theorem of Serre 160
Zariski theorem 85
Zariski topology 10 108
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