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Voisin C. — Hodge theory and complex algebraic geometry 2
Voisin C. — Hodge theory and complex algebraic geometry 2

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Название: Hodge theory and complex algebraic geometry 2

Автор: Voisin C.

Аннотация:

The first volume of this book was devoted to the study of the cohomology of compact Kahler manifolds. The main results there can be summarised as follows. (Throughout this volume, we write for example vl.6.1 to refer to volume I, section 6.1.)


Язык: en

Рубрика: Математика/Алгебра/Алгебраическая геометрия/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2003

Количество страниц: 351

Добавлена в каталог: 07.05.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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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 $CH_0(A)$      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 $CH_0$      13 284
Roitman theorem on the torsion in the group $CH_0$      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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