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Fulton W. Ч Intersection theory
Fulton W. Ч Intersection theory

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Ќазвание: Intersection theory

јвтор: Fulton W.

язык: en

–убрика: ћатематика/јлгебра/јлгебраическа€ геометри€/

—татус предметного указател€: √отов указатель с номерами страниц

ed2k: ed2k stats

»здание: 2-nd edition

√од издани€: 1984

 оличество страниц: 470

ƒобавлена в каталог: 23.03.2005

ќперации: ѕоложить на полку | —копировать ссылку дл€ форума | —копировать ID
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ѕредметный указатель
Abel Ч Jacobi map      14 387 390
Abelian variety      14 60 219
Adjunction formula      59 289 301
Affine bundle      22
Algebraic equivalence      185Ч186 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      383Ч384
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      268Ч279 386
BezoutТs theorem for plane curves      14
BezoutТs theorem, classical version      101 144Ч152
BezoutТs theorem, refined      223Ч226
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 Ч Roch for      365Ч366
Blow-up      435Ч437 439
Blow-up formula      114Ч117
Borsuk Ч Ulam theorem      239Ч240
Canonical class      67 300 302
Canonical class of singular variety      77Ч79
Canonical class, divisor      60 301 432
Canonical decomposition of intersection product      94Ч95 200Ч205 218Ч226
Cap product      131
Cap product for Borel Ч Moore homology      371 374Ч375
Cap product, refined      132Ч136 324Ч326
Cartesian product      24Ч25 428
Cartier divisor(s)      29 431Ч432
Cartier divisor(s), addition of      29
Cartier divisor(s), canonical section of      432
Cartier divisor(s), effective      19Ч20 30 432
Cartier divisor(s), intersection by      33Ч41
Cartier divisor(s), line bundle of      31Ч32 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      31Ч32
Cartier divisor(s), support of      30Ч31 432
Cartier divisor(s), Weil divisor of      29Ч32
Castelnuovo Ч Severi inequality      311Ч312
Cellular decomposition      23 25 378
Characteristic of a family of varieties      188 Ч194
Characteristic, homomorphism      199
Characteristic, section      199
Characteristic, variety      73
Chasles Ч Cayley Ч Brill Ч Hurwitz formula      310
Chern character      56Ч57 282Ч284
Chern character in topology      367
Chern character, localized      340Ч355 363Ч366
Chern class(es) of $\mathbb{P}^n$      59
Chern class(es) of dual bundle      54
Chern class(es) of exterior power      55 265
Chern class(es) of line bundle      41Ч43 51
Chern class(es) of non-singular variety      60
Chern class(es) of normal bundle      59Ч61
Chern class(es) of P(E)      59
Chern class(es) of singular varieties      77Ч79 376Ч377
Chern class(es) of symmetric powers      57 265
Chern class(es) of tensor products      54Ч56 265
Chern class(es) of vector bundles      50Ч63 252 255Ч256
Chern class(es) of virtual bundles      57 296
Chern class(es), blowing up      298Ч303
Chern class(es), geometric construction of      252 255Ч256
Chern class(es), localized      255
Chern class(es), localized of complex      347
Chern class(es), localized, top      244Ч246
Chern class(es), MacPherson      376Ч377
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 216Ч217 365 367
Chern number      293Ч294
Chern polynomial      50
Chern roots      54
Chow ring      141 (see also УIntersection ringФ)
Chow variety      16Ч17 186
circle      192
Class of hypersurfaces      84Ч85
Class of non-singular variety      84Ч85 253 261Ч262 277Ч278
Class of plane curve      188
Class of surface      193
Codimension      427
Coefficient of a variety in a cycle      11
Cohen Ч Macaulay      81 120 137 226 251 418Ч419
Cohomology for rational equivalence      143 324Ч326 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      35Ч38
Commutativity for intersection multiplicities      123
Commutativity for intersection products      106Ч107 132
Compact supports for rational equivalence      184 368 378
Complete algebraic scheme      429
Complex of vector bundles      431
Complex, perfect      365Ч366
Conductor      167 289
Cone(s)      70 432Ч434
Cone(s) of sheaf      73
Cone(s), construction, for moving lemma      206
Cone(s), exact sequence of      72Ч73
Cone(s), normal      71 73 435
Cone(s), projective      432Ч434
Cone(s), projective completion of      70
Cone(s), pull-back of      433
Cone(s), Segre class of      70Ч73
Cone(s), support of      433Ч434
Cone(s), zero section of      433
Conics, plane      63Ч64 157Ч158 182Ч183 187Ч194 204 275
Conservation of number      180Ч185 193Ч194
Contribution of variety to an intersection product      94Ч95 151 224Ч225
Correspondence(s)      308Ч318 384Ч385 390Ч391
Correspondence(s) of morphism      306
Correspondence(s) on $\mathbb{P}^n$      315Ч316
Correspondence(s) on curves      310Ч312
Correspondence(s) on Grassmannians      317
Correspondence(s) on surfaces      317
Correspondence(s), (a, b)-      309
Correspondence(s), birational      312
Correspondence(s), degenerate      308Ч309
Correspondence(s), degree (or codimension) of      308
Correspondence(s), fixed points of      315Ч318
Correspondence(s), indices (or degrees) of      309
Correspondence(s), irreducible      306
Correspondence(s), principle      310
Correspondence(s), product of      305Ч308
Correspondence(s), push-forward and pull-back of      307
Correspondence(s), ring of      307Ч308
Correspondence(s), SeveriТs formula for      317
Correspondence(s), topological      384Ч385
Correspondence(s), transpose of      306
Correspondence(s), valence of      309Ч310
Correspondence(s), Zeuthen, generalized      310
Critical point, moderate      246
Critical point, multiplicity of      124Ч125
Curve(s), rational normal      84 156
Curve(s), tangent to given varieties      187Ч194
Cycle, class      10
Cycle, class homomorphism or map      371Ч378
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      378Ч385
Cycle, fundamental      15
Cycle, k-      10
Cycle, non-negative, positive      10 180 211
Cycle, of subscheme      15
Deformation      198Ч200
Deformation to normal cone or bundle      86Ч91
Deformation, generic      201Ч205
Degeneracy, class      254Ч263 329 330
Degeneracy, class, positivity of      260Ч261
Degeneracy, class, symmetric and skew-symmetric      216 259Ч260
Degeneracy, locus      243
Degeneracy, locus, existence of      215Ч216
Degree of cycle or equivalence class      13
Degree of cycle or variety on P"      42 144 149Ч150
Degree of Schubert variety      274
Degree, L-      211
Depth      251Ч252 255 256 418Ч419
Determinant      409Ч412
Determinantal class      249Ч253
Determinantal formula      249Ч253
Determinantal identities      419Ч424
Determinantal locus      243 419
Differentials, relative      429Ч430
DIMENSION      427
Dimension, pure      427
Dimension, relative      429
Dimension, relative for schemes over regular base      394 396
Distinguished varieties      94Ч95 120Ч121 184 200Ч205 218Ч226 232
Double point, class      166
Double point, formula      165Ч171 289
Double point, scheme      166Ч168
Double point, set      166
Dual variety, degree of      62Ч63 84 144 169Ч170
Duality for flag manifolds      276Ч277
Duality for Grassmann bundles      267 269 270 271
Duality, Grothendieck      367Ч368
Duality, Poincare      281 328 398 440
Duality, Serre      291 368
Dynamic intersections      128 195Ч209
Enumerative geometry      187Ч194 272Ч279
Envelope, Chow envelope      356
Equivalence of connected component      153Ч160
Equivalence of variety for an intersection product      94Ч95 203Ч204
Equivalence, relations on cycles      374 385Ч392
Euler characteristic of fibres of map      245Ч246
Euler characteristic of non-singular variety      60 136 362
Euler obstruction      78 376
Exact sequence for closed and open subschemes      21Ч22 186
Exact sequence for monoidal transforms      115
Exceptional divisor      435Ч436
Excess, intersection formula      102Ч106 113 327 382
Excess, intersection of divisors      36
Excess, normal bundle      102 113 225
Extension of ground field      101Ч102 240
Exterior products      24Ч25 397
Families of cycles and cycle, classes      176Ч180 362
Fano varieties, schemes      80 217 275Ч276
Fibre, product      428
Fibre, square      428
Fixed points of correspondence, perfect      315Ч317
Fixed points of correspondence, virtual number of      315
Flag bundle      68 247Ч248
Flag manifold or variety      23 68 219 270 276Ч277 310
Flat      413 (see also УMorphism flatФ)
Function field      427
Functoriality of Gysin maps      108Ч112 113 134 330
Functoriality of intersection products      108Ч112
Functoriality of intersection products on non-singular varieties      130Ч136 141
Functoriality of push-forward and pull-back      11 18
General position      440Ч441
Genus of curve      60
Genus, Todd      60
Giambelli formula      262 265 267Ч268 271
Graph construction for complexes of vector bundles      340Ч346
Graph construction for vector bundle homomorphisms      88 347Ч348
Grassmann bundle      248Ч249 266Ч270 434
Grassmann variety      23 219 271Ч279
Grassmann variety of lines in $\mathbb{P}^3$      272Ч273
Grothendieck group of sheaves      17 281 285Ч286 354
Grothendieck group of vector bundles      57 280Ч281 294Ч295
Gysin formulas for flag bundles      247Ч248
Gysin formulas for Grassmann bundles      248Ч249
Gysin formulas for projective bundles      66
Gysin homomorphism for divisors      43Ч45
Gysin homomorphism for l.c.i. morphisms      113
Gysin homomorphism for morphisms to non-singular varieties      131 134 208
Gysin homomorphism for regular imbeddings      89Ч90 98 101
Gysin homomorphism for zero section of bundle      65Ч67 100
Gysin homomorphism or map from bivariant classes      328
Gysin homomorphism, refined      97Ч102 112Ч114 131 134
Herbrand quotients      407Ч411
Higher direct image      281
Higher K-theory      151 356 403Ч405
Hilbert Ч Samuel polynomial      42 81
Hodge theory      387Ч388
Homogeneous varieties      207 219Ч221 378 441
Homological equivalence      374 385Ч388
Homology theory for rational equivalence      10 324
Homology theory for topological K-theory      367
Homology theory, Borel Ч Moore      371 374Ч375
Hyperplane at infinity      433
Imbedding      426
Imbedding, obstructions to      60Ч61
Incidence correspondence or variety      189 273 275 277 295
Index theorem      289Ч290 388Ч389
Intermediate Jacobian      80 387 390
Intersecting with a pseudo-divisor      38
Intersecting, transversally      138 206 441
Intersection class      see УIntersection productФ
Intersection class of cycle and pseudo-divisor      33 38
Intersection class, analytic      383Ч384
Intersection class, infinitesimal      199
Intersection class, positivity of      218Ч223
Intersection class, refined      94
Intersection class, topological      378 381Ч385
Intersection multiplicity or number for divisors      38Ч40 123Ч124 232Ч233 400
Intersection multiplicity or number for divisors and curves      125Ч126
Intersection multiplicity or number for plane curves      7Ч10 14
Intersection multiplicity or number of Serre      401Ч403
Intersection multiplicity or number on non-singular varieties      137Ч139 227Ч234
Intersection multiplicity or number on schemes over Dedekind rings      398
Intersection multiplicity or number on surfaces      40Ч41
Intersection multiplicity or number, fractional      125 142Ч143
Intersection multiplicity or number, uniqueness of      139 207
Intersection product and Tor      401Ч403
Intersection product for curves on a surface      60 76 95Ч96 198 203
Intersection product for divisors      111 208 224
Intersection product on $\mathbb{P}^n$      144Ч151 202Ч203
Intersection product on non-singular varieties      130Ч136
Intersection product on schemes over Dedekind rings      397Ч401
Intersection product on singular surfaces      39Ч40 125 142
Intersection product, part supported on a set      95 100Ч101 201Ч202 222
Intersection ring of $\mathbb{P}^n$      144Ч145
Intersection ring of algebraic scheme      324
Intersection ring of Cartesian product      141
Intersection ring of flag manifold      276Ч277
Intersection ring of Grassmann variety      270
Intersection ring of monoidal transform      142
Intersection ring of multiprojective space      146
Intersection ring of non-singular variety      140Ч144 151Ч152
Intersection ring of projective bundle      141
Intersection ring of quasi-projective scheme      143 324
Intersection ring of scheme over a Dedekind ring      397Ч399 405
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