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| Ïîèñê ïî óêàçàòåëÿì |
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| Fulton W. — Intersection theory |
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| Ïðåäìåòíûé óêàçàòåëü |
Inverse image scheme 428
Irreducible components of intersection 120 148—149
Jacobian subscheme 84 168—169
Jacobian variety 14 17 79—80 256—257 309
Key formula 114
Kodaira-Spencer homomorphism 199
Koszul complex 121—122 282 414—416 431
Lefschetz fixed point theorem 314
Length 8 120—122 137 145 363 406—407 411
Limit, cycle 196
Limit, intersection class, cycle 197
Limit, set 196
Line bundle 431
Linear system(s) and Segre classes 82—85
Linear system(s) on curves 43 262—263
Linear system(s), base of 83
Linear system(s), tangents to 61—62
Linkage (liaison) 59 165 173
Linking numbers 383
Littlewood — Richardson rule 265 267 271 423
Local complete intersection (l.c.i.) 112—114 439
Local ring of scheme along subvariety 426—427
Manin’s identity principle 312—313
Milnor number 124 245—246
Monoidal transform 114—117 142 298—302 435—437
Morphism 427—430
Morphism, birational 428
Morphism, dominant 427—428
Morphism, finite 429
Morphism, flat 18 429
Morphism, flat of relative dimension n 429
Morphism, local complete intersection (l.c.i.) 112—114 439
Morphism, perfect 286 367
Morphism, proper 11 429
Morphism, separated 428—429
Morphism, smooth 429—438
Motives 312—313
Moving Lemma 26 205—209
Multiple point formula 160 171
Multiplicity along a subscheme 81
Multiplicity along a subvariety 79—82 231
Multiplicity at a point 79—82 227—234
Multiplicity of a module w.r.t. endomorphism 407—411 415—416
Multiplicity, algebraic 79—82
Multiplicity, geometric 15
Multiplicity, one, criterion for 81 126—127 137—138 207 230
Multisecants 159—160
Neron — Severi group 385 388 400—401
Noether’s formula 230
Non-singular imbeddings into 438 439
Non-singular variety, scheme 130—152 429—430
Normal bundle 43 435 437—438
Normal cone 73 85—86 435—436
Normal cone, projectivized 433—434 436
Normal domain 419
Normal variety 429
Normalization 9 429
Numerical equivalence 374 376 383
Numerical equivalence, finite generation of 375—376
Order of zeros and poles 8—10
Order, function for domain 411—412
Orientation(s), orientation class(es) 326—331
Orientation(s), orientation class(es) for cones 336
Orientation(s), orientation class(es) for flat morphisms 326
Orientation(s), orientation class(es) for imbeddings of manifolds 372—373
Orientation(s), orientation class(es) for l.c.i. morphisms 326—327 382
Orientation(s), orientation class(es) for monoidal transforms 332—333
Orientation(s), orientation class(es) for morphisms to smooth schemes 329
Orientation(s), orientation class(es) for perfect morphisms 367
Orientation(s), orientation class(es) for regular imbeddings 326 378—379
Orientation(s), orientation class(es), compatibility of 330
Osculation 43
P-field 237—241
Partition 236
Partition, conjugate 263—264
Picard group 14 30 331
Picard variety 385
Pieri formula 264 266 271 422—423
Pieri theorem 315—316
Pinch point 168—170
Plucker formula 43
Point 7 427
Point, rational 427
Point, regular 427
Polar classes of hypersurface 84—85
Polar classes of non-singular variety 226—227 261—262
Polar locus 261—262
Polar surface 170
Polar variety 226—227
Porteous formula 254—263
Porteous formula, excess 258
Positivity of intersection products 210—234
Principal lines 315
Principal parts 43 144
Principal tangents 315
Principle of continuity 180—185 193—194 207
Projection 47 428 433
Projection formula for bivariant classes 323
Projection formula for Chern classes 41 51 53
Projection formula for divisors 34 39
Projection formula for intersection multiplicities 123 207
Projection formula for intersection products 98 132 134 135 140
Projection formula for sheaves 281
Projective bundle 434
Projective bundle, cycle class of 61
Projective bundle, rational equivalence on 64—65
Projective characters 252—253
Projective completion of cone or bundle 433
Proper component of intersection product 120 137 138
Proper intersection 35 119—126 136 137—139 205—209
Pseudo-divisor(s) 31—32
Pseudo-divisor(s) of Carrier divisor 31
Pseudo-divisor(s), line bundle of 31
Pseudo-divisor(s), pull-back of 32
Pseudo-divisor(s), section of 31
Pseudo-divisor(s), sums of 32
Pseudo-divisor(s), support of 31
Pseudo-divisor(s), Weil divisor class of 32
Pull-back flat, of cycles or cycle classes 18—21 113 134
Pull-back for pseudo-divisors 32
Pull-back for regular imbeddings or l.ci. morphisms see “Gysin maps”
Pull-back from non-singular varieties 131 329
Push-forward, proper, of cycles and classes 11—14
Quadric surfaces 141 192—193
Quotient variety 20—21 23—24 142—143 313—314 331
Ramification 62 82 125 164—165 170—171 174 258
Rank 253 261—262 273
Rational equivalence 10 15—17 25—27 31
Rational equivalence for local rings 396
Rational equivalence on schemes 394 396
Real algebraic schemes 240—241
Real closed field 235—241
Real forms 240
Reduction to diagonal 130—131 151—152
Regular imbedding 437—438
Regular local ring 126—127 137 418
Regular section 414 431
| Regular sequence 416—418
Residual intersection class 162 163 221 231—232
Residual intersection formula for top Chern class 245
Residual intersection theorem 160—165 333—337
Residual scheme 160—161 164—165 437
Residual scheme, normal cone to 163—164
Residue 384 389
Resolution of sheaf 281—282 440
Resultant 8—9 150—152 410—411 424
Riemann hypothesis for curves 312
Riemann — Hurwitz formula 62
Riemann — Kempf formula 79—80
Riemann — Roch 280—304 339—369
Riemann — Roch and Grothendieck duality 367—368
Riemann — Roch and specialization 400
Riemann — Roch and topological K-theory 367
Riemann — Roch and Tor 364—365
Riemann — Roch formula for complexes 363—365
Riemann — Roch, bivariant 365—366
Riemann — Roch, for abelian varieties 291 292
Riemann — Roch, for Cartesian products 360
Riemann — Roch, for curves 288—289 360
Riemann — Roch, for imbeddings 282—283 287—288 294 364 365
Riemann — Roch, for l.c.i. morphisms 349 353—354 363
Riemann — Roch, for projections 283 284—285 287 291—292 295 304
Riemann — Roch, for quasi-projective schemes 348—353
Riemann — Roch, for schemes over regular bases 395
Riemann — Roch, for singular varieties 339—369
Riemann — Roch, for surfaces 289 361
Riemann — Roch, for threefolds 290—291
Riemann — Roch, Grothendieck- 286 354
Riemann — Roch, Hirzebruch- 288—354
Riemann — Roch, homomorphism 287 349 353 357—359
Riemann — Roch, homomorphism, uniqueness of 354 360
Riemann — Roch, Lefschetz- 353
Riemann — Roch, without denominators 296—298 353
Ruled, join 147—152
Ruled, variety 143—144
Samuel multiplicity 79 81
Scheme(s) over a regular base 393—396
Scheme(s), algebraic 6 426
Scheme(s), smooth 429
Scheme(s), theoretic intersection 428
Schubert calculus 271—279
Schubert class 271
Schubert class, special 271 272
Schubert variety 269 270 271
Schubert variety in flag manifold 276—277
Schur polynomials (or S-functions) 216 217 243 263—266 419—424
Schur polynomials, skew 266 274
Scott, D. B., formula of 61
Section(s) of vector bundles 430—431 440—441
Section(s), sheaf of 430
Section(s), zero scheme of 430
Segre class of cone 70—73
Segre class of sheaf 73
Segre class of subscheme, subvariety 67 73—79 168—169
Segre class of vector bundle 47—49 63—64
Segre class, birational invariance of 74—76
Segre class, total 50
Segre imbedding 61 142 146
Self-intersection of divisors 67
Self-intersection, formula 44 60 103 167
Serre’s, intersection multiplicity 401—403 405
Serre’s, lemma 440—441
Seven’s formula 317
Signature 292—293 388—389
Singular (Jacobian) subscheme 84 168—169
Singularity of morphism 258 348
Singularity, effect on intersections 40 125 183
Singularity, ordinary 168—169
Singularity, Thom — Boardman 258
Smoothing cycles 297
Snapper polynomials 361
Solutions of equations, rationality and existence of 235—241
Special divisors 79—80 256—257
Special position, principle of 193
Specialization 33 105—106 176—180 398—401
Specialization of Segre classes 180
Specialization to normal cone 89—91
Splitting, construction 51
Splitting, principle 54—55
Stiefel — Whitney class 68 377
Subscheme, subvariety 6—7 426
Support of cycle 33
Support of divisor 30 31
Symmetric product of curves 27 79—80 180 262—263
Symmetric product of projective schemes 16—17 386
Tangent bundle 59—61 219—220 430
Tangent bundle, relative 429—430 438—439
Tangent bundle, relative, for projective and Grassrnann bundles 435
Tangent cone 227
Tangents to curves 187—194 133—134 273—274
Theta divisor 80
Thom — Porteous formula 254—263
Todd class of algebraic scheme 354 360—361
Todd class of curves 360
Todd class of fibres 362
Todd class of l.c.i. scheme 354
Todd class of non-singular variety 60 288 293
Todd class of surfaces 361
Todd class of vector bundle 56—57 283
Todd class ofcoverings 362—363
Todd genus 60
Tor 286
Tor and intersection products 401 —403
Tor and Riemann — Roch 364 401—403
Triple points 168—170
Unirational variety 179—180
Universal bundle 434
Vanishing theorems of Serre, Kodaira, Le Potier 291
Variety 6—7 426—427
Vector bundle(s), Chern class of 51—61
Vector bundle(s), direct sums of 430
Vector bundle(s), dual of 430
Vector bundle(s), exterior powers of 430
Vector bundle(s), locally free sheaf of 430
Vector bundle(s), pull-back of 430
Vector bundle(s), rational equivalence on 64
Vector bundle(s), Segre class of 47—50
Vector bundle(s), tautological, universal 434
Veronese, imbedding 60 63 146
Veronese, surface 60 157—158 187
Weil divisor of a rational function 10 30
Weil divisor, associated to a Cartier divisor 29—31
Weil divisor, associated to a pseudo-divisor 32
Whitney, sum formula 51 57—59
Whitney, umbrella 24
Young, diagram 263—264
Young, tableau 264
Young, tableau, expansion of 264—265
Zero scheme of section 243 430
Zero scheme of vector bundle homomorphism 243 439
Zero-cycles 16—17 386—387 390
Zero-divisors of bilinear forms 238
Zeuthen — Segre invariant 301
Zeuthen’s rule 9—10
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