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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
$\delta$-functor      205 219 234 238 240 243 282
$\mathbf{Proj}$      160—169
$\sigma$-Process      386
-Adic completion      193 254
-adic topology      33 213 279
-Uple embedding      13 21 54 155 156 159 167 183 291 343 385
-Uple embedding is projectively normal      126 315
Abelian category      202—206
Abelian category with enough injectives      204 217
Abelian variety      105 140 422 437 447 451 see
Abhyankar, Shreeram      391
Abstract nonsingular curve      42—46 108 136
Abstract nonsingular curve is quasi-projective      45
Abstract variety      58 105
Acyclic resolution      205
Additive functor      203
Adjoint functors      68 110 124
Adjunction formula      361 368 374 382 387 390
Affine coordinate ring      4 8 17 20 23
Affine curve      4 7 8 47
Affine curve, any noncomplete curve is      297 298
Affine curve, locally free sheaves on      385
Affine formal scheme      195
Affine formal scheme, global section functor is exact      198 199
Affine line, $A^1$      74
Affine line, $A^1$ is not proper      100
Affine line, $A^1$ with a point doubled      76 96 169
Affine morphism      128 222 252
Affine n-space, $A^n$      1
Affine n-space, $A^n$, automorphisms of      23
Affine plane, $A^2$      75
Affine scheme      59 74 124
Affine scheme is quasi-compact      80
Affine scheme, cohomology of      114 213—216
Affine scheme, criterion for      81 215 216
Affine scheme, global section functor is exact      113
Affine scheme, sheaf $\tilde{M}$ on      110—113
Affine variety      1—8 20 21 25
Algebraic equivalence of cycles      444
Algebraic equivalence of divisors      140 367 369
Algebraic family      see "Family"
Algebraic integer      330—332 450 457
Algebraic set      2 4 5 9 47
Algebraic space      445
Algebraizable formal scheme      195
Algebraizable sheaf      281
Altman, Allen      268
Ample divisor      see also "Ample invertible sheaf"
Ample divisor on a curve      156 307 308 372
Ample divisor on a surface      365 368 405
Ample divisor, Nakai — Moishezon criterion      356 365 382 405 434
Ample invertible sheaf      150 153—156 161 248
Ample invertible sheaf on $P^n$      155
Ample invertible sheaf on a curve      307 308 365
Ample invertible sheaf on a quadric surface      156
Ample invertible sheaf, cohomological criterion of      229
Ample invertible sheaf, existence of $\Rightarrow$ separated      169
Ample invertible sheaf, not very ample      156
Ample invertible sheaf, properties of      169 232
Ample invertible sheaf, scheme without an      169 171
Analytically isomorphic singularities      34 38 298 393—395
Annihilator      50 124
Arithmetic genus, $p_a$      54 57 201 230 232 246 268
Arithmetic genus, $p_a$ is a birational invariant      230 409 413
Arithmetic genus, $p_a$ of a $P(\mathscr{E})$      253
Arithmetic genus, $p_a$ of a complete intersection      54 231
Arithmetic genus, $p_a$ of a curve      54 181 246 294 298
Arithmetic genus, $p_a$ of a curve on a surface      366 389 401
Arithmetic genus, $p_a$ of a product      54
Arithmetic genus, $p_a$ of a surface      188 247 362 371 409 421
Arithmetic genus, $p_a$, constant in a family      263 265 289
Arithmetic genus, $p_a$, invariant by monoidal transformation      388 394
Artin ring      266
Artin, Michael      417 445 449 452 453
Assigned base point of a linear system      395 399 400
Associated point (of a scheme)      257
Atiyah, Michael, F.      378 383
Automorphisms of $A^n$      23
Automorphisms of $P^1$      46
Automorphisms of $P^n$      151 158 347
Automorphisms of a curve of genus $\geq 2$      305 348 349 368
Automorphisms of a curve of genus 3      348
Automorphisms of an elliptic curve      318 321 336
Automorphisms of k(x)      46
Automorphisms of the configuration of 27 lines      405 408
Baily, W.L., Jr.      349
Banica, Constantin      439
Base extension      89 254 265
Base extension, behavior of cohomology      282 290 326 369
Base extension, behavior of differentials      175
Base extension, flat      255 287
Base extension, stable under      90
Base for topology      25 71
Base points of a linear system      158 307 395
Base points, scheme of      169
Base scheme      89
Base-point free      158 307 318
Baum, Paul      436
Berthelot, Pierre      452
Bertini, E.      316
Bertini’s theorem      179 183 187 188 245 250 281 425
Bertini’s theorem in characteristic 0      268 274
Bertini’s theorem with singularities      180
Bertini’s theorem, gives nonsingular curves      183 231 314 342 358 381 406
Betti numbers      451 456
Bezout’s Theorem      47 54 146 361 400 417
Bilinear form      364
Binomial coefficient      49 52
Birational equivalence      24 26—31 45 55 181 314 370 418
Birational invariant      56 181 190 387 409 421
Birational morphism      56 166 280 310 313
Birational transformation      409—420
Birational transformation of a ruled surface      416
Birational transformation, defined at a point      410
Birational transformation, factorization of      386 409 411—413 416
Birational transformation, fundamental point of      410
Birationally ruled surface      370 383 419 see
Birch, B.J.      317 334
Bitangent      305
Blowing down lines      398 416
Blowing up      28—31 163—171 356 see
Blowing up is birational      29 166
Blowing up is intrinsic      166
Blowing up is not flat      258
Blowing up, a curve on a surface      388—394
Blowing up, a nonsingular subvariety      186 188 394 443
Blowing up, canonical sheaf of      188
Blowing up, curve singularities      29 37 390
Blowing up, Picard group of      188
Blowing up, strict transform under      see "Strict transform"
Blowing up, surfaces      56 395
Blowing up, to construct valuation rings      108 420
Blowing up, universal property of      164 412
Blowing up, vertex of cone      37 374 381
Bombieri, Enrico      356 421 451
Borel, Armand      149 239 432 435
Borelli, Mario      238
Branch divisor      306
Branch of a curve      30
Branch point      299 317
Branched covering      293
Brieskom, Egbert      420 421
Burnside, W.      349
Canonical curve      341 346 348 353 385
Canonical divisor on a curve      293 295 299 373
Canonical divisor on a hyperelliptic curve      343
Canonical divisor on a singular curve      298
Canonical divisor on a surface      361 373 387 421 424
Canonical embedding      293 340—349
Canonical linear system      340 341
Canonical morphism      341 422
Canonical sheaf, $\omega_X$      180 239 246
Canonical sheaf, $\omega_X$ of $P^n$      182
Canonical sheaf, $\omega_X$ of a blowing-up      188
Canonical sheaf, $\omega_X$ of a complete intersection      188 315
Canonical sheaf, $\omega_X$ of a curve      294 295
Canonical sheaf, $\omega_X$ of a hypersurface      183 184
Canonical sheaf, $\omega_X$ of a nonsingular subvariety      182
Canonical sheaf, $\omega_X$ of a product      187
Cardinality of a variety      31
Cartan, Henri      172
Cartan’s theorem B      211 441
Cartesian product (of graded rings)      125
Cartier divisor      140—146 231 see
Cartier divisor on a singular curve      142 148 298
Cartier divisor, algebraic family of      261
Cartier divisor, associated Weil divisor of      141
Cartier divisor, effective      145 427
Cartier divisor, linear equivalence of      141
Cartier divisor, principal      141
Cartier divisor, sheaf $\mathscr{L}(D)$ associated to      144
Cartier, Pierre      172
Cassels, J.W.S.      331 335
Castelnuovo, G.      351 368 422
Castelnuovo’s criterion for contracting a curve      356 410 414—417
Category Abelian      202—206
Category of abelian groups $\mathfrak{Ab}$      61
Category of open sets, $\mathfrak{Top}(X)$      61
Category of schemes over S, $\mathfrak{Qch}(S)$      78
Category of sheaves on X, $\mathfrak{Ab}(X)$      65
Category of varieties over k $\mathfrak{Bar}(k)$      78
Category, inverse limit in      192
Category, product in      22
Cech cocyle      232 240
Cech cohomology      201 211 218—225 255 262
Cech cohomology of a plane curve      224
Cech cohomology, computation of      219 220 225—227
Cech cohomology, computes $R^{'}f_*$      252 282
Cech cohomology, limit over coverings      223
Center of a valuation      106 108 137
Center of blowing up      163
Characteristic      2 312 317
Characteristic p      21 31 33 80 89 276 293 312 316 317 332—335 339 385 391 422 see
Characteristic p, funny curve in      305 385
Characteristic p, reduction mod p      89 334 340 451
Characteristic p, search for good cohomology      451
Characteristic zero      232 268 271—275 304 305 348 382 391 see
Chem class      363 425 429—431 433 435 437 450
Chem polynomial      429 435
Chem, S.S.      423
Chevalley, Claude      48 94 95 172 222 427 428
Chinese remainder theorem      138
Chow ring      426 428 429 433 437 454
Chow variety      349
Chow, Wei-Liang      105 324 441 443
Chow’s Lemma      107
Chow’s Moving Lemma      427 434
circle      213 220
Class field theory      331
Class of a curve      305
Classical projective geometry      403 407
Classification of curve singularities      38 393—395
Classification of curves      56 341 345—347
Classification of curves in $P^3$      349—355 354 409
Classification of curves of genus      2 304
Classification of elliptic curves      317 345
Classification of elliptic ruled surfaces      377
Classification of locally free sheaves of rank 2 on an elliptic curve      378
Classification of rational ruled surfaces      376 419
Classification of surfaces      56 421—423
Classification, problem      39 55—57 181 293 345
Clemens, C. Herbert      184 304
Clifford’s theorem      341 343 350 423
Closed immersion      85 92 see
Closed immersion is finite      124
Closed immersion is of finite type      93
Closed immersion is proper      102
Closed immersion is separated      99
Closed immersion, criterion for      151 152 158 307
Closed morphism      91 100
Closed points are dense      93
Closed subscheme      see also "Closed immersion"
Closed subscheme of a Proj      92 119 125
Closed subscheme of an affine scheme      85 92 111 116
Closed subscheme of codimension one      145
Closed subscheme with nilpotents      see "Nilpotent element"
Closed subscheme, associated Cartier divisor      145 149
Closed subscheme, associated cycle      425
Closed subscheme, completion along      86 190 194 279
Closed subscheme, criterion to be nonsingular      178
Closed subscheme, ideal sheaf of      115
Closed subscheme, image of a morphism      92
Closed subscheme, locally principal      145
Closed subscheme, reduced induced structure      86 92
Coarse moduli variety      347
Codimension      86 87
Coeffaceable functor      206 238 240 243
Cohen — Macaulay ring      184
Cohen — Macaulay scheme      185 239 243 276
Cohen, I.S.      34 187
Coherence of direct image sheaf      115
Coherence of direct image sheaf for a finite morphism      124
Coherence of direct image sheaf for a projective morphism      123 152 252 280
Coherent analytic sheaf      439 440 447
Coherent sheaf      111—115 see
Coherent sheaf, completion along a closed subscheme      194
Coherent sheaf, extending from an open set      126
Cohn-Vossen, S.      403
Cohomological dimension      224
Cohomology      see also "Cech cohomology"
Cohomology and base change      282 290 326 369
Cohomology of $P^1$      219
Cohomology of a circle      213 220
Cohomology of a complete intersection      231
Cohomology of a complex      203
Cohomology of an affine scheme      114 213—216
Cohomology of fibres      250 255 281 290
Cohomology of projective space      225—230
Cohomology of sheaves      206—211
Cohomology with supports      212 217
Cohomology, as a derived functor      207 211 439
Cohomology, Cech process      218—225
Cohomology, characterizes ample sheaf      154 229
Cohomology, class of a cycle      435 454
Cohomology, class of a divisor      367 418
Cohomology, class of a subvariety      249
Cohomology, commutes with $\underrightarrow{lim}$      209
Cohomology, commutes with flat base extension      255 287
Cohomology, crystalline      452
Cohomology, etale      307 452 453
Cohomology, functor      207
Cohomology, gives numerical invariants      57 230 246 247
Cohomology, group      207 424
Cohomology, l-adic      435 449 452—457
Cohomology, p-adic      452
Cohomology, Picard group as      143 224 367 446
Cohomology, theories      211 449
Cokernel      63 65 109
Complete intersection      14 188 452
Complete intersection is connected      188 231
Complete intersection is every curve?      14
Complete intersection, a divisor on a quadric hypersurface is      147
Complete intersection, arithmetic genus of      54 231
Complete intersection, canonical sheaf of      188 315
Complete intersection, cohomology of      231
Complete intersection, curve      38 342 346 352 355
Complete intersection, elliptic quartic curve is      38
Complete intersection, geometric genus of      188
Complete intersection, hyperelliptic curve is not      348
Complete intersection, hyperplane section of      267
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