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Hartshorne R. — Algebraic Geometry
Hartshorne R. — Algebraic Geometry



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Название: Algebraic Geometry

Автор: Hartshorne R.

Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: 8th

Год издания: 1997

Количество страниц: 496

Добавлена в каталог: 12.06.2007

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Nonsingular variety      31—39 130 177—180 268 424 see "Smooth
Nonsingular variety, $\Omega$ is locally free      177 178 276
Nonsingular variety, hyperplane section of      see "Bertini’s theorem"
Nonsingular variety, infinitesimal lifting property      188
Nonspecial divisor      296 343 349
Norm (of a field extension)      46
normal      see also "Projectively normal"
Normal $\Leftrightarrow$ $R_1 + S_2$      185
Normal bundle      see "Normal sheaf"
Normal crossings, divisor with      391
Normal cuspidal cubic curve is not      23
Normal point      23 38
Normal quadric surface is      23 147
Normal ring      185 264
Normal scheme      91 126 130 244 280
Normal sheaf, $\mathscr{N}_{Y/X}$      182 361 386 431 433 436 see
Normal variety      23 263 410
Normalization      23 91 426
Normalization of a curve      148 232 258 298 343 365 382
Number theory      58 316 451 452
Numerical equivalence      364 367 369 435
Numerical invariant      56 256 361 372 379 425 433
Numerical polynomial      49
Olson, L.      140
Open affine subset      25 106
Open immersion      85
Open set $X_f$      81 118 151
Open subscheme      79 85
Ordinary double point      see "Node"
Ordinary inflection point      305 see
Ordinary r-fold point      38 305
Osculating hyperplane      337
p-adic analysis      451
p-Adic cohomology      452
p-Linear map      332
Parameter space      56 see
Parametric representation      7 8 22 260
Paris seminar      436 449
Pascal’s theorem      407
Pencil      280 422
Perfect field      27 93 187
Period mapping      445
Period parallelogram      326
Petri, K.      348
Picard group, Pic X      57 143 232 250 357 428 see
Picard group, Pic X of a $P(\mathscr{E})$      170 291
Picard group, Pic X of a blowing-up      188
Picard group, Pic X of a cubic surface in $P^3$      401
Picard group, Pic X of a family      323
Picard group, Pic X of a formal scheme      200 281
Picard group, Pic X of a line with point doubled      169
Picard group, Pic X of a monoidal transformation      386
Picard group, Pic X of a nonprojective variety      171
Picard group, Pic X of a product      292 338 367
Picard group, Pic X of a projective variety over $\mathbb{C}$      447
Picard group, Pic X of a ruled surface      370
Picard group, Pic X of a singular curve      148
Picard group, Pic X of an elliptic curve      297 323
Picard group, Pic X, as $H^1(X,\mathscr{O}_X^*)$      143 224 367 446
Picard group, Pic X, Lefschetz theorem      190
Picard group, Pic X, torsion elements of      306
Picard variety      140 447
Pinch point      36
Plane curve      7 35—39 304 305 319 407
Plane curve with nodes      310—316 337 348
Plane curve, birational to a curve with ordinary singularities      407
Plurigenus, $P_n$      190 422
Poincare duality      453 456
Point, closed      74 75 81 93
Point, embedded      85 259
Point, open      74
Point, rational over k      see "Rational points"
Pole of a rational function      130 131 297
Polynomial equations      55
Polynomial equations over finite fields      449
Presheaf      61 62 109 193
Prime divisor      130
Prime ideal      4 11 22 70 76 132
Primes in an arithmetic progression      335
Primitive element, theorem of      27
Principal divisor      131 141 367
Principal divisor has degree zero      132 138
Principal ideal domain      254
PRODUCT      see also "Direct product"
Product in a category      22 66 87
Product of curves      44 338 367
Product of schemes      87
Product of varieties      22
Product, arithmetic genus of      54
Product, canonical sheaf of      187
Product, Cartesian of graded rings      125
Product, differentials on      187
Product, fibred      87 100
Product, morphism      99
Product, Picard group of      292 338 367
Product, Segre embedding of      see "Segre embedding"
Product, topological space of      91
Product, Zariski topology on      7
Proj      76 77
Proj of a graded homomorphism      80 92
Proj, closed subschemes of      92 119 125
Proj, sheaves of modules on      116—123 125
Projection from a linear space      169
Projection from a point      22 151 259 309—316
Projection of a twisted cubic curve      22
Projection, birational      30 31 310
Projection, formula      124 253 380 419 426 431
Projection, morphism      87
Projective closure      12
Projective cone      see "Cone"
Projective dimension      237
Projective general linear group, PGL      46 151 273 347
Projective module      238 284
Projective morphism      103 107 123 149—172 277 281 290
Projective n-space, $P^n$      8 10 77 103 120 151 155 225—230
Projective object (in a category)      205 237
Projective resolution      205 236
Projective scheme      103 120 121 232
Projective space bundle      170 171 186
Projective space bundle, associated to a locally free sheaf, $P(\mathscr{E})$      162—169
Projective space bundle, canonical sheaf of      253
Projective space bundle, Chow ring of      429
Projective space bundle, cohomology of      253
Projective space bundle, Picard group of      170 291
Projective space bundle, ruled surface as      370
Projective variety      8—14
Projectively normal      23 126 147 159 188 267
Projectively normal, canonical curve is      348
Projectively normal, curve      23 231 315 336 354 355
Projectively normal, d-uple embedding is      126
Proper intersection      427
Proper morphism      95—108 161 252 279
Proper morphism is closed      100 152
Pure transcendental field extension      303
Purely inseparable      302 305 385
Quadratic number field      330—332 334 340
Quadratic transformation      30 31 397 398 403 406 408 409 see
Quadric cone      23 133 134 142 346 352 428
Quadric cone, curves on      384
Quadric hypersurface      38 55
Quadric hypersurface, divisor class group of      147
Quadric surface      13 14 23 30
Quadric surface, 2-uple embedding of      401
Quadric surface, ample sheaves on      156 366
Quadric surface, as a ruled surface      369 381
Quadric surface, canonical sheaf of      183
Quadric surface, cohomology of      231
Quadric surface, curves on      231 294 346 351 352 354 362 381
Quadric surface, divisor class group of      133 135
Quadric surface, intersection theory on      361 364
Quartic curve      see also "Curve of degree 4"
Quartic curve has 28 bitangents      305
Quartic curve, elliptic      38 315 353
Quartic threefold is not rational      184
Quasi-affine variety      3 21 223
Quasi-coherent sheaf      111—115 126 see
Quasi-compact morphism      91
Quasi-compact scheme      80 119
Quasi-compact topological space      8 80
Quasi-finite morphism      91 280 366
Quasi-projective morphism      103
Quasi-projective variety      10
Quotient sheaf      65 109 141
Quotient topology      75
Radical ideal      4
Radical of an ideal      3
Ramanujam, C.P.      249
Ramanujan $\tau$-function      452
Ramification divisor      301 382
Ramification index      299
Ramification point      299
Ramified morphism      299 312
Ramis, J.P.      249
Rank      109 148
Rational curve      46 55 138 143 297 315 343 345 see "Twisted
Rational curve, elliptic curve is not      46 139 183
Rational equivalence of cycles      425 426 436 454
Rational function      16 30 46 297 419
Rational function, divisor of      130 131 294
Rational map      24—31 168
Rational normal curve      315 343
Rational numbers, $\mathbb{Q}$      58 148 335
Rational points      80
Rational points on an elliptic curve      317 335 336 339
Rational points over a finite field      368 449
Rational quartic curve      23 159 231 291 315 353 386
Rational ruled surface      369 379—381 see
Rational ruled surface of degree 3 in $P^4$      170 348 381 397 437
Rational ruled surface, blow-up of $P^2$      375 381 397
Rational ruled surface, classification of      376 419
Rational ruled surface, embedded in $P^n$      381 385 437
Rational surface      56 170 422 see "Veronese
Rational surface, blow-up of $P^2$      375 381 395 397 400 406 408
Rational variety      30 183 184
Rationality of plane involutions      422
Rationality of the zeta function      449 450 452
Raynaud, Michel      249
Real numbers, $\mathbb{R}$      4 8 80 106
Reduced induced structure      86 92
Reduced inverse image divisor      391
Reduced scheme      79 82 365
Reduction mod p      89 334 340 451
Reduction to the diagonal      427 428
Refinement of a covering      223
Regular function      15 21 23 30 42 62 70
Regular in codimension one      130 185
Regular local ring      32 38 40 130 136 237 238 243 415
Regular local ring is Cohen — Macaulay      184
Regular local ring is UFD      142
Regular local ring, $\Leftrightarrow \Omega$ is free      174 187
Regular local ring, complete      34
Regular local ring, localization of is regular      177
Regular q-forms, sheaf of, $\Omega^q_{X/k}$      247 249
Regular scheme      142 170 179 238 268 275 see "Smooth
Regular sequence      184 217 245 261
Relative cohomology      250
Relative differentials      see "Differentials"
Relative dimension      268
Relative projective space      162
Relative tangent sheaf      436
Relatively minimal model      see "Minimal model"
Remmert, Reinhold      442
Repartitions      248
Representable functor      241 324
Residue      239 247 248
Residue field      22 80
Resolution by Cech complex      220
Resolution of singularities      28 55 168 386 390 391 413 420 442 453
Resolution of singularities, embedded      390 391 392 419
Resolution, acyclic      205
Resolution, fine      201
Resolution, flasque      201 208 212 248
Resolution, injective      204 242
Resolution, locally free      149 234 239
Resolution, projective      205 236
Restriction of a sheaf to a subset, $\mathscr{F}|_Z$      65 112
Restriction of sections of a sheaf      61 118
Riemann existence theorem      442
Riemann hypothesis      339 368 449—452 457 458
Riemann surface      338 441 447
Riemann zeta function      457
Riemann — Roch problem      170 296 424
Riemann — Roch theorem on a 3-fold      437
Riemann — Roch theorem on a curve      156 249 293—299 317 325 341 343 349 362 376 424 432
Riemann — Roch theorem on a singular curve      298
Riemann — Roch theorem on a surface      356 357 362—364 366 423 424 433
Riemann — Roch theorem, generalized      57 149 170 363 424 431—436
Riemann, Bernhard      446
Riemenschneider, Oswald      249 445
Right derived functor      204 207 233 250
Right exact functor      204 286
Rigid algebra      267
Rigid scheme      267
Ring of dual numbers      80 265 267 324
Ring of endomorphisms of an elliptic curve      323 329 330 338 340
Ring of integers in a number field      330 331
Ring of regular functions      16—18 21
Ring, spectrum of      70—75 110—113
Ringed space      72 143 see
Ringed space, sheaf of modules on      109 110 123 124 127 233
Roberts, Joel      427
Root systems      408
Roquette, P.      306
Rossi, Hugo      69 201 438
Ruget, G.      249
Ruled surface      56 170 253 356 369—385 373 422 see
Ruled surface, ample divisors on      380 382 383
Ruled surface, arithmetic genus of      371
Ruled surface, birationally      370 419
Ruled surface, blown-up cone      374 381
Ruled surface, canonical divisor of      373
Ruled surface, elementary transformation of      416 419
Ruled surface, elliptic      369 375 377 384 385 440
Ruled surface, embedded in $P^n$      381 385
Ruled surface, geometric genus of      371
Ruled surface, intersection theory on      370
Ruled surface, invariant $K^2$      374
Ruled surface, invariant e      372 374—377 384
Ruled surface, nonsingular curves on      380
Ruled surface, normalized      373
Ruled surface, Picard group of      370
Ruled surface, sections of      371 373 379 383—385
Ruled surface, stable      379
Ruled surface, very ample divisors on      379 380 383 385
Ruled surface, zero-cycles on      437
Ruling on a quadric cone      133 134 428
Saint-Donat, Bernard      344 348
Sally, Judith      412
Samuel, Pierre      312 394 420 428
Satellite functor      206
Saturation of a homogeneous ideal      125
Scheme      59 69—82
Scheme of finite type over a field      93
Scheme over $\mathbb{R}$      106
Scheme over another scheme      78
Scheme, associated complex analytic space      see "Complex analytic space"
Scheme, associated to a variety      78 84 104 136
Scheme, connected      82 see
Scheme, geometrically integral      93
Scheme, geometrically irreducible      93
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