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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
Scheme, geometrically reduced      93
Scheme, glueing of      75 80 91 171 439 444
Scheme, integral      82 91
Scheme, irreducible      82
Scheme, locally factorial      141 145 148 238
Scheme, locally noetherian      83
Scheme, Noetherian      83
Scheme, nonprojective      171 232 443
Scheme, nonseparated      76 96
Scheme, nonsingular in codimension one      130
Scheme, normal      see "Normal"
Scheme, reduced      79 82 365
Scheme, regular in codimension one      130 185
Scheme-theoretic closure      258
Scheme-theoretic image      92
Scheme-theoretic intersection      171 358
Schlaefli’s double-six      403
Schlessinger, Michael      185 266 267
Schwarz’s inequality      402
Scott, D.B.      431
SCROLL      381 385
Secant line      309 316
Secant line not a multisecant      314 316 351
Secant line with coplanar tangents      310
Secant variety      310 316
Section      see also "Global sections"
Section of a morphism      129 170 369
Section of a presheaf      61
Section, discontinuous, sheaf of      67
Segre embedding      13 22 54 107 125 126 156
Self-intersection      360 386 401 437 450
Self-intersection formula      431 433
Self-intersection of the canonical divisor, $K^2$      361 367 374 387 421
Semi-linear automorphism      106
Semicontinuity theorem      281—292 354 369
Semistable      384
Separable field extension      27 300 422
Separable morphism      300
Separably generated field extension      27 174 187 271
Separate points      152 158 308 380
Separate tangent vectors      152 158 308 380
Separated morphism      95—108
Separated scheme      76 96 106 119 130 169
Separating transcendence base      27
Serre duality      181 239—249 293—295 362 363 367 419 424
Serre, Jean-Pierre      51 57 121 149 154 185 201 211 215 228 239 247 249 297 307 330 331 335 366 422 427 428 432 435 440 446 447 451 452
Seshadri, C.S.      379
Set-theoretic complete intersection      14 224
Seven, Francesco      47 244 314 316 368
SGA      436 449 462
Shafarevich, I.R.      356 369 383 410 421
Shannon, David, L.      412
Sheaf      60—69
Sheaf of $\mathscr{O}_Y$-algebras      128
Sheaf of discontinuous sections      67
Sheaf of graded algebras      160
Sheaf of modules      108—129 233
Sheaf of rings      62 70
Sheaf of total quotient rings      141
Sheaf, $\tilde{M}$ associated to a module      110—113 116
Sheaf, associated to a presheaf      64 250
Sheaf, free      109
Sheaf, generated by global sections      121 150—156 307 358 365
Sheaf, glueing      69 175
Sheaf, Horn      67 109
Sheaf, inverse image of      65 110 115 128 299
Shioda, T.      422
Siegel, Carl Ludwig      442
Signature      364
Simple group of order 168      349
Simple group of order 25920      405
Simple group of order 60      420
Simply connected scheme      303 304 340
Singh, Balwant      306
Singular locus      390
Singular point      32 33 35 36
Singular point of a cone, blowing up      37 374 381
Singular point of a curve on a surface      386
Singular point of a surface      36 420
Singular point, analytically isomorphic      34 38 298 393
Singular point, moving in a linear system      276
Singular point, multiplicity of      see "Multiplicity"
Singular point, resolution of      see "Resolution of singularities"
Skew commutative graded algebra      127
Skyscraper sheaf      68 296
slope      30
Smooth morphism      268—276 303
Space curves      349
Special divisor      296
Special divisor, existence of      345
Special linear system dimension of      see "Clifford’s theorem"
Specialization      93 97 354
Spectral sequence      236 252 289
Spectrum of a ring, Spec A      70—75 82
Spectrum of a ring, Spec A, sheaf $\tilde{M}$ on      110—113
Spectrum of a sheaf of algebras, $\mathbf{Spec}$      128 280 306
Spencer, D.C.      414
Splitting principle      430
Square-free polynomial      147
Stable image      191
Stable locally free sheaf      379 384
Stable ruled surface      379
Stable under base extension      90 93 99 102 107
Stable under generization      94 266
Stable under specialization      94 98
Stalk      62 71 76 124
Stanasila, Octavian      439
Standard conjectures of Grothendieck      435
Stein factorization      276 280 366
Stein space      216 440
Steiner prize      349
Stepanov, S.A.      451
Stereographic projection      420
Stichtenoth, H.      306
Strange curve      311 316
Strict transform      30 31 165 171 381 388 390 406 see
Strong Lefschetz theorem      452
Structure sheaf      74 111
Submodule with supports $\Gamma_O(M)$      124 213
Subscheme, open      79 85
Subsheaf      64
Subsheaf with supports $\mathscr{H}^O_Z(\mathscr{I})$      68
Subvariety      21 425
Subvariety, cohomology class of      249
Subvariety, local ring of      22 58
Suominen, Kalevi      249
Superabundance      362
Supersingular elliptic curve      332
Support      67 124 212 215 217
surface      4 105
Surface in $P^4$      170 348 381 397 433 434 437
Surface of degree d in $P^4$      170 348 381 397 437
Surface of degree d in $P^d$      401
Surface of degree d in $P^{d+1}$      381
Surface of general type      184 422 423
Surface with infinitely many exceptional curves      409 418
Surface, $P^2$ with 1 point blown up      375 381 397
Surface, $P^2$ with 2 points blown up      406
Surface, $P^2$ with 3 points blown up      397
Surface, $P^2$ with 5 points blown up      408
Surface, $P^2$ with 6 points blown up      395 400
Surface, algebraic equivalence of divisors      367 369
Surface, complete intersection      409 423 437
Surface, cubic      see "Cubic surface in $P^3$"
Surface, definition for Ch. II      105
Surface, definition for Ch. V      357
Surface, Del Pezzo      401 408
Surface, divisor on      135 357
Surface, elliptic      422
Surface, elliptic ruled      see "Elliptic ruled surface"
Surface, Enriques      422
Surface, factorization of birational transformations      386 409 411—413 416
Surface, geometry on      357—368
Surface, group Num X      364 367 368
Surface, invariant $K^2$      361 367 374 387 421
Surface, K3      184 422 423 437 452
Surface, lines on      13 136 367 402—406 408
Surface, minimal model of      see "Minimal model"
Surface, product of two curves      338 367 368
Surface, rational      see "Rational ruled surface" "Rational
Surface, valuation rings of      108 420
Surface, Veronese      13 170 316 381
Sylvester, J.J.      364
Symmetric algebra of a module      127 162 374
Symmetric function      431
Symmetric group      304 318 408
Symmetric product of a module      127 185
Tacnode      36 37 39 305 348
Tame ramification      299
Tangent bundle      57 450 see
Tangent direction      36
Tangent line      54 139 148 304 309 337
Tangent sheaf, $\mathscr{J}_X$      180 182 225 265 363 425 431 437
Tangent variety      310
Tate, John, T.      247 317 335 451 452
Tensor algebra      127
Tensor operations      127
Tensor product, $\otimes$      22 87 109 127 153 430
Thickened fibre      277
Three-fold      105 184 437
Tjurin, Andrei      383
Todd class      432
Topological covering space      442
Topological space, axiom $T_0$      93
Topological space, dimension of      5 see
Topological space, disconnected      82
Topological space, generic point of      74 75 80 93
Topological space, irreducible      3
Topological space, quasi-compact      8 80
Topological space, set of irreducible closed subsets of      78
Topological space, underlying a scheme      74
Topology of algebraic varieties over $\mathscr{C}$      421
Topology, Etale      452 453
Topology, Hausdorff      2 8 95 439
Topology, quotient      75
Topology, Zariski      2 5 7 10 14 70
Tor group      427 428
Torsion sheaf      149 372
Torus      328 442 447
Total Chem class      429
Total quotient ring      141
Total transform      410
Trace map      241 247 249 307 453 455
Trace of a linear system      158
Transcendence base      27
Transcendence degree      6 27 421
Transcendental methods      289 326 367 438—448
Transversal intersection      357—360 392 425 427
Triangulable      447
Trigonal curve      345
Triple point      36
Trisecant      346 348
Trotter, H.      334
Tsen’s theorem      369
Twenty-seven lines      402—406
Twisted cubic curve      7 12—14 159 315 353
Twisted cubic curve, conormal sheaf of      385
Twisted cubic curve, not a complete intersection      14 136
Twisted cubic curve, projection of      22 259
Twisted module, M(n)      50
Twisted quartic curve      see "Rational quartic curve"
Twisted sheaf, $\mathscr{F}(n)$      117
Twisted sheaf, $\mathscr{F}(n)$, cohomology vanishes      228
Twisted sheaf, $\mathscr{F}(n)$, generated by global sections      121
Twisting sheaf $\mathscr{O}(1)$      117 120 225
Twisting sheaf $\mathscr{O}(1)$ on $P(\mathscr{E})$      162
Twisting sheaf $\mathscr{O}(1)$ on $\mathbf{Proj}\mathscr{I}$      160
Twisting sheaf $\mathscr{O}(1)$, generated by global sections      150
Twisting sheaf $\mathscr{O}(1)$, generates Pic $P^n$      145
Twisting sheaf $\mathscr{O}(1)$, not very ample      171
Type (a,b) of a divisor on a quadric surface      135
Unassigned base point of a linear system      395
Uncountable field      409 417
Underlying topological space      74
Uniformizing parameter      258 see
Union of two planes      224 266 267 428
Unique factorization domain, UFD      7 46 131 141 147 420
Universal $\delta$-functor      205 238 243
Universal parameter space      323 347 see
Universally closed morphism      100
Unmixedness theorem      188
Unramified morphism      275 299 see
Upper semi-continuous function      125 287 291
Valuation      39 43 299
Valuation of a prime divisor      130 135
Valuation ring      40 97 101 105 see
Valuation ring, examples of      108 420
Valuation ring, nondiscrete      108
Valuation, center of      106
Valuative criterion of properness      101 107 181 259 325 410
Valuative criterion of separatedness      97 107
Vanishing theorem of Grothendieck      208
Vanishing theorem of Kodaira      248 249 408 423 424 445
Vanishing theorem of Nakano      445
Vanishing theorem of Serre      228 424
Variety of moduli      56 58 266 317 346 421
Variety over k      15 78
Variety, abstract      58 105
Variety, algebraic family of      see "Family"
Variety, complete      see "Complete variety"
Variety, isomorphisms of      16 18
Variety, morphisms of      14—23
Variety, nonprojective      171 443
Variety, normal      see "Normal"
Variety, projectively normal      see "Projectively normal"
Variety, quasi-affine      3 21 223
Variety, scheme associated to      78 84 104
Vector bundle      128 170 see
Vector bundle, sheaf of sections of, $\mathscr{S}{X/Y)$      129
Verdier, Jean-Louis      249
Veronese surface      13 170 316 381
Vertex of a cone      37 394 see
Very ample divisors      307 308 358
Very ample divisors form a cone      359
Very ample invertible sheaf      120 126 153—156 228 236
Very ample invertible sheaf on $\mathbf{Proj}\mathscr{I}$      161
Very ample invertible sheaf on a curve      307
Very flat family      266
Virtual arithmetic genus      367
Vitushkin, A.G.      23
Walker, R.J.      391 393
Weierstrass $\wp$-function      327
Weil cohomology      453
Weil Conjectures      449—458
Weil conjectures, cohomological interpretation of      454—457
Weil divisor      130—136 294 426 428 436 see
Weil, Andre      48 58 105 248 368 428 435 445 449—452 454
Weyl group      405 408
Weyl, Hermann      441
Wild ramification      299
Witt vectors      452
Zariski space      93 94 213
Zariski tangent space      37 80 158 265 270 324
Zariski topology      2 5 7 10 14 70
Zariski topology is not Hausdorff      2 95
Zariski topology, base of open affine subsets      25
Zariski topology, weaker than usual topology      439
Zariski, Oscar      32 57 58 60 105 170 190 244 276 356 391 393 394 410 419 422
Zariski’s main theorem      57 276 280 410 412
Zeros common      35
1 2 3 4 5 6 7
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