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| Hartshorne R. — Algebraic Geometry |
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| Предметный указатель |
Hypersurface, any variety is birational to 27
Hypersurface, arithmetic genus of 54
Hypersurface, canonical sheaf of 183 184
Hypersurface, complement of is affine 21 25
Hypersurface, existence of nonsingular 183
icosahedron 420
Ideal class group 132
Ideal of a set of points 3 10
Ideal of definition 196
Ideal sheaf,  109
Ideal sheaf, of a closed subscheme 115 116 120 145
Ideal sheaf, of a subvariety 69
Ideal sheaf, of denominators 167
Ideal sheaf, , blowing up 163 171
Idempotent 82
Igusa, Jun-ichi 265 334
Image of a morphism of sheaves 63 64 66
Image of a proper scheme is proper 106
Image, scheme-theoretic 92
Immersion 120
Immersion, open 85
Indecomposable locally free sheaf 376 384
Index of a bilinear form 364
Index of speciality 296
Induced structure of scheme 79 86 92
Induced structure of variety 21
Inequality of Castelnuovo and Severi 368 451
Infinitely near point 392 395
Infinitesimal deformation see "Deformation"
Infinitesimal extension 189 225 232 265
Infinitesimal lifting property 188
Infinitesimal neighborhood 86 190 276 393
Inflection point 139 148 304 305 335 337
Inflection point, cubic curve has 9 305 322
Initial object 80
Injective module 206 207 213 214 217
Injective object (of a category) 204 217 233
Injective resolution 204 242
Injective sheaf 207 213 217
Inseparable morphism 276 311 312
Integers,  79 340
Integral closure 40 91 105
Integral closure, finiteness of 20 38 123
Integral scheme 82 91
Integrally closed domain 38 40 126 132 147 see
Intersection divisor 135 146 261
Intersection multiplicity 36 47 53 233 304 357 360 394 427
Intersection number 357—362 366 394 445
Intersection of affines is affine 106
Intersection of varieties 14 21 47—55
Intersection theory 47—55 58 424—437
Intersection theory on  361 see
Intersection theory on a cubic surface 401
Intersection theory on a monoidal transform 387
Intersection theory on a nonsingular quasi-projective variety 427
Intersection theory on a quadric surface 361 364
Intersection theory on a ruled surface 370
Intersection theory on a singular variety 428
Intersection theory on a surface 356—362 366 425
Intersection theory, axioms 426
Intersection, proper 427
Intersection, scheme-theoretic 171 358
Invariant theory 420
Inverse image ideal sheaf,  163 186
Inverse image of cycles 426
Inverse image of divisors, f* 135 137 299
Inverse image, sheaf,  110 115 128 299
Inverse image, sheaf,  65
Inverse limit,  in a category 192
Inverse limit, of abelian groups 190—192 277
Inverse limit, of rings 33
Inverse limit, of sheaves 67 109 192
Inverse system 190
Invertible sheaf 109 117 118 124 143—146 169
Invertible sheaf on a family 291
Invertible sheaf, associated to a divisor 144 145 157 294 425
Invertible sheaf, determines a morphism to  150—153 158 162 307 318 340
Invertible sheaf, extension of 372 375 376 383 430
Invertible sheaf, generated by global sections 150—156 307 358 365
Invertible sheaf, group of see "Picard group"
Involution 106 306
Irreducible closed subset 78 80
Irreducible component 5 7 11 47 365
Irreducible scheme 82
Irreducible topological space 3 4 8 11
Irregularity 247 253 422
Irrelevant ideal 11
Iskovskih, V.A. 184 304
Isogeny of elliptic curves 338
Isolated singularity 420
Italians 391
j-Invariant of an elliptic curve 316—321 331 345 347
Jacobian matrix 32
Jacobian polynomial 23
Jacobian variety 105 140 316 323—326 338 445 447 see
Jouanolou, J.P. 436
K3 surface 184 422 423 437 452
Kaehler differentials see "Differentials"
Kaehler manifold 445 446 452
Kernel 63 64 109
Kleiman, Steven, L. 144 238 268 273 345 434 435 452 453
Klein, Felix 147 349 420
Knutson, Donald 445
Kodaira dimension 421 422
Kodaira vanishing theorem 248 249 408 423 424 445
Kodaira, Kunihiko 249 266 409 414 422 442 443
Koszul complex 245 389
Krull dimension 6 86 see
Krull — Akizuki, theorem of 108
Krull, Wolfgang 213 279
Krull’s Hauptidealsatz 7 48
Kunz, E. 249
Kuyk, W. 317 334
l-adic cohomology 435 449 452—457
l-Adic integers 338 453
Laksov, D. 345
Lang, Serge 140 334 364 367 452
Lascu, A.T. 431
Lattice 326
Lefschetz fixed-point formula 453 454
Lefschetz pencil 457
Lefschetz Theorem 190 281
Lefschetz theorem, strong 452
Lefschetz, Solomon 451
Left derived functor 205
Left exact functor 113 203 284 286
Length of a module 50 290 360 394
Leray spectral sequence 252
Leray, theorem of 211
Lichtenbaum, Stephen 185 267
Lie group 328
Line 22 28 129 183 see "Secant "Tangent
Line on a surface 13 136 367 402—406 408
Linear equivalence 57 131 141 294 425 426 see
Linear equivalence  algebraic equivalence 367
Linear projection see "Projection"
Linear system 130 150 156—160 274
Linear system of conics 170 396—398
Linear system of plane cubic curves 399 400
Linear system on a curve 307
Linear system with assigned base points 395
Linear system, complete 157 159 170 294
Linear system, determines a morphism to 158 307 318
Linear system, dimension of 157 295 357 424
Linear system, not composite with a pencil 280
Linear system, separates points 158 308 380
Linear system, separates tangent vectors 158 308 380
Linear system, very ample 158 307 308 396
Linear system, without base points 158 307 341
Linear variety 13 38 48 55 169 316 see
| Lipman, Joseph 249 391 420
Local cohomology see "Cohomology with supports"
Local complete intersection 8 184—186 245 428 see
Local criterion of flatness 270
Local homomorphism 72 74 153
Local parameter 137 258 299
Local ring of a point 16—18 22 31 41 62 71 80
Local ring of a subvariety 22 58
Local ring, complete 33—35 187 275 278 420
Local ring, local homomorphism of 72 74
Local space 213
Locally closed subset 21 94
Locally factorial scheme 141 145 148 238
Locally free resolution 149 234 239
Locally free sheaf 109 124 127 178
Locally free sheaf of rank 2 356 370 376 378 437
Locally free sheaf on a curve 369 370 379 384
Locally free sheaf on an affine curve 385
Locally free sheaf, as an extension of invertible sheaves 372 375 376 383 430
Locally free sheaf, Chern classes of see "Chern class"
Locally free sheaf, decomposable 376 378 383 384
Locally free sheaf, dual of 123 143 235 430
Locally free sheaf, indecomposable 376 384
Locally free sheaf, projective space bundle of see "Projective space bundle"
Locally free sheaf, resolution by 149 234 239
Locally free sheaf, stable 379 384
Locally free sheaf, trivial subsheaf of 187
Locally free sheaf, vector bundle  of 128 170
Locally free sheaf, zeros of a section 157 431
Locally Noetherian scheme 83
Locally principal closed subscheme 145
Locally principal Weil divisor 142
Locally quadratic transformation 386
Locally ringed space 72 73 169 see
Logarithmic differential, dlog 250 367 457
Lubkin, Saul 452
Lueroth’s Theorem 303 422
Macbeath, A.M. 306
MacPherson, R.D. 436
Manifold 31 see
Manin, Ju, I. 149 184 304 401 405 408 436 452
Maruyama, Masaki 383
Matsumura, Hideyuki 123 172 184 195 250 268 418
Mattuck, Arthur 451
Maximal ideal 4
Mayer — Vietoris sequence 212
Mayer, K.H. 421
Meromorphic function 327 442
Minimal model 56 410 418 419 421
Minimal polynomial 147
Minimal prime ideal 7 50 98
Mittag-Leffler condition, (ML) 191 192 200 278 290
Module flat 253
Module free 174
Module of finite length 50 290 360 394
Moduli, variety of 56 58 266 317 346 421
Moishezon manifold 442—446
Moishezon manifold, nonalgebraic 444
Moishezon, Boris 366 434 442 443 446
monodromy 457
Monoidal transformation 356 386—395 409 410 414 443 see
Monoidal transformation, ample divisor on 394
Monoidal transformation, behavior of a curve 388—394
Monoidal transformation, behavior of arithmetic genus 387—389
Monoidal transformation, behavior of cohomology groups 387 419
Monoidal transformation, canonical divisor of 387
Monoidal transformation, Chow ring of 437
Monoidal transformation, intersection theory on 387
Monoidal transformation, local computation 389
Monoidal transformation, Picard group of 386
Mordell, L.J. 335
Morphism of finite type 84 91 93 94
Morphism of Spec K to X 80
Morphism, affine 128 222 252
Morphism, closed 91 100
Morphism, determined by an open set 24 105
Morphism, dominant 23 81 91
Morphism, etale 268 275 276 299
Morphism, generically finite 91 436
Morphism, glueing of 88 150
Morphism, injective of sheaves 64
Morphism, inseparable 276 311 312
Morphism, locally of finite type 84 90
Morphism, projective 103 107 123 149—172 277 281 290
Morphism, quasi-compact 91
Morphism, quasi-finite 91 280 366
Morphism, quasi-projective 103
Morphism, ramified 299 312
Morphism, smooth 268—276 303
Morphism, surjective of sheaves 64 66
Morphism, to , etermined by an invertible sheaf 150—153 158 162 307 318 340
Morphism, universally closed 100
Morphism, unramified 275 299 see
Morrow, James 266 442
Moving Lemma 425 427 434
Moving singularities 276
Multiple tangent 305
Multiplicity 36 51 388 393 394 see
Multisecant 310 355
Mumford, David 140 249 291 324 336 347 356 366 379 417 419—421 431 437
Nagata, Masayoshi 58 87 105 108 168 381 383 384 394 401 409 419
Nakai — Moishezon criterion 356 365 382 405 434
Nakai, Yoshikazu 144 366 434
Nakano, Shigeo 249 445
Nakayama’s Lemma 125 153 175 178 288
Narasimhan, M.S. 379
Natural isomorphism 240
Negative definite 368 419
Neron — Severi group 140 367 418
Neron — Severi group is finitely generated 447
Neron — Severi theorem 364 367 368
Neron, Andre 367
Nilpotent element see also "Dual numbers ring
Nilpotent element in a ring 79—81
Nilpotent element in a scheme 79 85 190 259 277 315
Nilradical of a ring 82
Nodal cubic curve 259 263 276
Nodal cubic curve is rational 30
Nodal cubic curve, blown up 29
Nodal cubic curve, divisor class group of 148
Node 36 37 258 293 298 392 394 see
Node, analytic isomorphism of 34 38
Node, plane curve with 310—316
Noether, Max 349
Noetherian formal scheme 194
Noetherian hypotheses 100 194 201 213—215 218
Noetherian Induction 93 94 214
Noetherian ring 80
Noetherian scheme 83
Noetherian topological space 5 8 11 80 83 see
Nonalgebraic complex manifold 444
Nonhyperelliptic curve 340 see
Nonhyperelliptic curve, existence of 342 345 385
Nonprojective scheme 232
Nonprojective variety 171 443
Nonsingular cubic curve is not rational 46 139 183 230
Nonsingular cubic curve, ample sheaves on 156
Nonsingular cubic curve, canonical sheaf of 183
Nonsingular cubic curve, divisor class group of 139
Nonsingular cubic curve, group law on 139 147 297 417
Nonsingular cubic curve, has 9 inflection points 305 322
Nonsingular curve 39—47 136
Nonsingular curve, divisors on 129
Nonsingular curve, existence of 37 231 352 406
Nonsingular curve, Grothendieck group of 149
Nonsingular curve, morphism of 137
Nonsingular curve, projective  complete 136
Nonsingular in codimension one 130
Nonsingular points 32 37
Nonsingular points form an open subset 33 178 187
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