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| Ïîèñê ïî óêàçàòåëÿì |
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| Fulton W. — Intersection theory |
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| Ïðåäìåòíûé óêàçàòåëü |
Abel — Jacobi map 14 387 390
Abelian variety 14 60 219
Adjunction formula 59 289 301
Affine bundle 22
Algebraic equivalence 185—186 373
Algebraic scheme 6 426
Ample, line bundle 211
Ample, vector bundle 212
Ample, vector bundle, generically 217
Ample, vector bundle, n-ample 215
Analytic space 383—384
Arithmetic genus and Todd class 288 354 361 362
Arithmetic genus, birational invariance of 292 294
Arithmetic genus, modular law 292
Arithmetic genus, uniqueness 292 293
Associativity for intersection multiplicities 123 129
Associativity for intersection products 132
Axioms for intersection products 97 207
Basis Theorem 268—279 386
Bezout’s theorem for plane curves 14
Bezout’s theorem, classical version 101 144—152
Bezout’s theorem, refined 223—226
Bidegree 146
Bivariant rational equivalence class(es) for schemes 395
Bivariant rational equivalence class(es), Gysin maps for 328
Bivariant rational equivalence class(es), products of 322
Bivariant rational equivalence class(es), pull-back of 322
Bivariant rational equivalence class(es), push-forward of 322
Bivariant rational equivalence class(es), Riemann — Roch for 365—366
Blow-up 435—437 439
Blow-up formula 114—117
Borsuk — Ulam theorem 239—240
Canonical class 67 300 302
Canonical class of singular variety 77—79
Canonical class, divisor 60 301 432
Canonical decomposition of intersection product 94—95 200—205 218—226
Cap product 131
Cap product for Borel — Moore homology 371 374—375
Cap product, refined 132—136 324—326
Cartesian product 24—25 428
Cartier divisor(s) 29 431—432
Cartier divisor(s), addition of 29
Cartier divisor(s), canonical section of 432
Cartier divisor(s), effective 19—20 30 432
Cartier divisor(s), intersection by 33—41
Cartier divisor(s), line bundle of 31—32 432
Cartier divisor(s), linear equivalence of 30
Cartier divisor(s), local equations for 29 432
Cartier divisor(s), principal 30 432
Cartier divisor(s), representing a pseudo-divisor 31—32
Cartier divisor(s), support of 30—31 432
Cartier divisor(s), Weil divisor of 29—32
Castelnuovo — Severi inequality 311—312
Cellular decomposition 23 25 378
Characteristic of a family of varieties 188 —194
Characteristic, homomorphism 199
Characteristic, section 199
Characteristic, variety 73
Chasles — Cayley — Brill — Hurwitz formula 310
Chern character 56—57 282—284
Chern character in topology 367
Chern character, localized 340—355 363—366
Chern class(es) of  59
Chern class(es) of dual bundle 54
Chern class(es) of exterior power 55 265
Chern class(es) of line bundle 41—43 51
Chern class(es) of non-singular variety 60
Chern class(es) of normal bundle 59—61
Chern class(es) of P(E) 59
Chern class(es) of singular varieties 77—79 376—377
Chern class(es) of symmetric powers 57 265
Chern class(es) of tensor products 54—56 265
Chern class(es) of vector bundles 50—63 252 255—256
Chern class(es) of virtual bundles 57 296
Chern class(es), blowing up 298—303
Chern class(es), geometric construction of 252 255—256
Chern class(es), localized 255
Chern class(es), localized of complex 347
Chern class(es), localized, top 244—246
Chern class(es), MacPherson 376—377
Chern class(es), Mather 79
Chern class(es), polynomials in 42 53 141
Chern class(es), polynomials in positive 216
Chern class(es), total 50 60
Chern class(es), uniqueness of 53
Chern class(es), vanishing of 50 216—217 365 367
Chern number 293—294
Chern polynomial 50
Chern roots 54
Chow ring 141 (see also “Intersection ring”)
Chow variety 16—17 186
circle 192
Class of hypersurfaces 84—85
Class of non-singular variety 84—85 253 261—262 277—278
Class of plane curve 188
Class of surface 193
Codimension 427
Coefficient of a variety in a cycle 11
Cohen — Macaulay 81 120 137 226 251 418—419
Cohomology for rational equivalence 143 324—326 331 390
Cohomology for rational equivalence with supports 325
Cohomology, operations 377
Coincidences, virtual number of 309
Commutativity for Chern classes 41 50
Commutativity for divisors 35—38
Commutativity for intersection multiplicities 123
Commutativity for intersection products 106—107 132
Compact supports for rational equivalence 184 368 378
Complete algebraic scheme 429
Complex of vector bundles 431
Complex, perfect 365—366
Conductor 167 289
Cone(s) 70 432—434
Cone(s) of sheaf 73
Cone(s), construction, for moving lemma 206
Cone(s), exact sequence of 72—73
Cone(s), normal 71 73 435
Cone(s), projective 432—434
Cone(s), projective completion of 70
Cone(s), pull-back of 433
Cone(s), Segre class of 70—73
Cone(s), support of 433—434
Cone(s), zero section of 433
Conics, plane 63—64 157—158 182—183 187—194 204 275
Conservation of number 180—185 193—194
Contribution of variety to an intersection product 94—95 151 224—225
Correspondence(s) 308—318 384—385 390—391
Correspondence(s) of morphism 306
Correspondence(s) on 315—316
Correspondence(s) on curves 310—312
Correspondence(s) on Grassmannians 317
Correspondence(s) on surfaces 317
Correspondence(s), (a, b)- 309
Correspondence(s), birational 312
Correspondence(s), degenerate 308—309
Correspondence(s), degree (or codimension) of 308
Correspondence(s), fixed points of 315—318
Correspondence(s), indices (or degrees) of 309
Correspondence(s), irreducible 306
Correspondence(s), principle 310
Correspondence(s), product of 305—308
Correspondence(s), push-forward and pull-back of 307
Correspondence(s), ring of 307—308
Correspondence(s), Severi’s formula for 317
Correspondence(s), topological 384—385
Correspondence(s), transpose of 306
Correspondence(s), valence of 309—310
Correspondence(s), Zeuthen, generalized 310
Critical point, moderate 246
Critical point, multiplicity of 124—125
| Curve(s), rational normal 84 156
Curve(s), tangent to given varieties 187—194
Cycle, class 10
Cycle, class homomorphism or map 371—378
Cycle, class homomorphism or map and Gysin maps 382
Cycle, class homomorphism or map and specialization 400
Cycle, class homomorphism or map and topological intersections 378—385
Cycle, fundamental 15
Cycle, k- 10
Cycle, non-negative, positive 10 180 211
Cycle, of subscheme 15
Deformation 198—200
Deformation to normal cone or bundle 86—91
Deformation, generic 201—205
Degeneracy, class 254—263 329 330
Degeneracy, class, positivity of 260—261
Degeneracy, class, symmetric and skew-symmetric 216 259—260
Degeneracy, locus 243
Degeneracy, locus, existence of 215—216
Degree of cycle or equivalence class 13
Degree of cycle or variety on P" 42 144 149—150
Degree of Schubert variety 274
Degree, L- 211
Depth 251—252 255 256 418—419
Determinant 409—412
Determinantal class 249—253
Determinantal formula 249—253
Determinantal identities 419—424
Determinantal locus 243 419
Differentials, relative 429—430
DIMENSION 427
Dimension, pure 427
Dimension, relative 429
Dimension, relative for schemes over regular base 394 396
Distinguished varieties 94—95 120—121 184 200—205 218—226 232
Double point, class 166
Double point, formula 165—171 289
Double point, scheme 166—168
Double point, set 166
Dual variety, degree of 62—63 84 144 169—170
Duality for flag manifolds 276—277
Duality for Grassmann bundles 267 269 270 271
Duality, Grothendieck 367—368
Duality, Poincare 281 328 398 440
Duality, Serre 291 368
Dynamic intersections 128 195—209
Enumerative geometry 187—194 272—279
Envelope, Chow envelope 356
Equivalence of connected component 153—160
Equivalence of variety for an intersection product 94—95 203—204
Equivalence, relations on cycles 374 385—392
Euler characteristic of fibres of map 245—246
Euler characteristic of non-singular variety 60 136 362
Euler obstruction 78 376
Exact sequence for closed and open subschemes 21—22 186
Exact sequence for monoidal transforms 115
Exceptional divisor 435—436
Excess, intersection formula 102—106 113 327 382
Excess, intersection of divisors 36
Excess, normal bundle 102 113 225
Extension of ground field 101—102 240
Exterior products 24—25 397
Families of cycles and cycle, classes 176—180 362
Fano varieties, schemes 80 217 275—276
Fibre, product 428
Fibre, square 428
Fixed points of correspondence, perfect 315—317
Fixed points of correspondence, virtual number of 315
Flag bundle 68 247—248
Flag manifold or variety 23 68 219 270 276—277 310
Flat 413 (see also “Morphism flat”)
Function field 427
Functoriality of Gysin maps 108—112 113 134 330
Functoriality of intersection products 108—112
Functoriality of intersection products on non-singular varieties 130—136 141
Functoriality of push-forward and pull-back 11 18
General position 440—441
Genus of curve 60
Genus, Todd 60
Giambelli formula 262 265 267—268 271
Graph construction for complexes of vector bundles 340—346
Graph construction for vector bundle homomorphisms 88 347—348
Grassmann bundle 248—249 266—270 434
Grassmann variety 23 219 271—279
Grassmann variety of lines in  272—273
Grothendieck group of sheaves 17 281 285—286 354
Grothendieck group of vector bundles 57 280—281 294—295
Gysin formulas for flag bundles 247—248
Gysin formulas for Grassmann bundles 248—249
Gysin formulas for projective bundles 66
Gysin homomorphism for divisors 43—45
Gysin homomorphism for l.c.i. morphisms 113
Gysin homomorphism for morphisms to non-singular varieties 131 134 208
Gysin homomorphism for regular imbeddings 89—90 98 101
Gysin homomorphism for zero section of bundle 65—67 100
Gysin homomorphism or map from bivariant classes 328
Gysin homomorphism, refined 97—102 112—114 131 134
Herbrand quotients 407—411
Higher direct image 281
Higher K-theory 151 356 403—405
Hilbert — Samuel polynomial 42 81
Hodge theory 387—388
Homogeneous varieties 207 219—221 378 441
Homological equivalence 374 385—388
Homology theory for rational equivalence 10 324
Homology theory for topological K-theory 367
Homology theory, Borel — Moore 371 374—375
Hyperplane at infinity 433
Imbedding 426
Imbedding, obstructions to 60—61
Incidence correspondence or variety 189 273 275 277 295
Index theorem 289—290 388—389
Intermediate Jacobian 80 387 390
Intersecting with a pseudo-divisor 38
Intersecting, transversally 138 206 441
Intersection class see “Intersection product”
Intersection class of cycle and pseudo-divisor 33 38
Intersection class, analytic 383—384
Intersection class, infinitesimal 199
Intersection class, positivity of 218—223
Intersection class, refined 94
Intersection class, topological 378 381—385
Intersection multiplicity or number for divisors 38—40 123—124 232—233 400
Intersection multiplicity or number for divisors and curves 125—126
Intersection multiplicity or number for plane curves 7—10 14
Intersection multiplicity or number of Serre 401—403
Intersection multiplicity or number on non-singular varieties 137—139 227—234
Intersection multiplicity or number on schemes over Dedekind rings 398
Intersection multiplicity or number on surfaces 40—41
Intersection multiplicity or number, fractional 125 142—143
Intersection multiplicity or number, uniqueness of 139 207
Intersection product and Tor 401—403
Intersection product for curves on a surface 60 76 95—96 198 203
Intersection product for divisors 111 208 224
Intersection product on 144—151 202—203
Intersection product on non-singular varieties 130—136
Intersection product on schemes over Dedekind rings 397—401
Intersection product on singular surfaces 39—40 125 142
Intersection product, part supported on a set 95 100—101 201—202 222
Intersection ring of 144—145
Intersection ring of algebraic scheme 324
Intersection ring of Cartesian product 141
Intersection ring of flag manifold 276—277
Intersection ring of Grassmann variety 270
Intersection ring of monoidal transform 142
Intersection ring of multiprojective space 146
Intersection ring of non-singular variety 140—144 151—152
Intersection ring of projective bundle 141
Intersection ring of quasi-projective scheme 143 324
Intersection ring of scheme over a Dedekind ring 397—399 405
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