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IItaka S. — Algebraic Geometry: An Introduction to Birational Geometry of Algebraic Varieties |
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Предметный указатель |
65 289
66 289
-space 13 15 25 241
-calculus 307
269
298
271
309
-topology 16
-homomorphism 29
-ideals 59
-module 28—29
-module, coherent 47—48 181 230
-module, finite type 46
-module, free 44
-module, quasi-coherent 45
-homomorphism 42
-modules associated with M 42
Abelian variety 308 312
Adjunction formula 201
Adjunction formula, generalized 204—205
Affine algebraic curve 51
Affine algebraic group 340
Affine algebraic variety 51 100
Affine morphism 88—89 94
Affine n-space 42 100
Affine Noetherian scheme 50
Affine open cover 55
Affine open subset 54
Affine scheme 4 41 179
Affine scheme, algebraic 51
Affine scheme, integral 51
Affine scheme, morphism of 53
Affine scheme, reduced 50—51
algebraic 19 87
Algebraic affine scheme 51
Algebraic boundary 99
Algebraic over R 87
Algebraic torus 326
Algebraic variety 95
ample 156 235
Ample divisor 156
Ample divisor, very 156 216—217
Ample, f- 239
Ample, R- 236
Arithmetic Euler — Poincare characteristic 182
Arithmetic genus 182
Artinian local ring 26
Artinian ring 26
Auslander Buchsbaum 120
Automorphism group 65
Base extension 71 75 77 86 89 91 93
Base extension of L 151
Base extension, locus 128
Base extension, number 266
Base extension, point 128
Base extension, scheme 65
Bertini 250
Bigenus 199
Birational automorphism group 96
Birational map 96
Birationally equivalent 96
Birationally equivalent, proper 137
Canonical derivation 188—189
Canonical divisor 199 208
Canonical fibered variety 311
Canonical homomorphism 10 34 145
Canonical involution 224
Canonical projection 64
Canonical rational map 200
Cartier sheaf 153
Castelnuovo 265 297
Category of S-schemes 65
Characteristic pair, first 285
Characteristic pairs of a cusp 285
Characteristic polynomials 113
Chinese remainder theorem 26 143
Chow's Lemma 137 170
Class of a curve 294
Clebsch 280
Clifford 213
Closed image 83
Closed immersion 61 71—72 76 86 89—93 241
Closed morphism 90
Closed morphism, universally 90
Closed point 15 20 84
Closed subscheme 60
Closure 14 15
Closure, scheme 92
Codimension 22
Cohen 23
Coherence, local property of 49
Coherent 47—48 181 230
Cohomology 176 226 230
Cokernel 36
complete 92 94—95 100
Complete linear system 127
Complete local ring 113
Completion 99 113 258
Composition of morphisms 52
Composition of rational maps 82
Conductor 204-205
Connectedness theorem of Zariski 138
Constant sheaf 28 152
Coordinate cover 196
Coordinate neighborhood 195
Coordinate system, local 195
Covering theorem 304 311 341
Covering, double 216—218
Covering, r-sheeted 216
Curve 100 208
Curve, affine algebraic 51
Curve, hyperelliptic 217
Cusp 281
Cusp, simple 281
D-canonical fibered variety 303
D-dimension 298
D-index 220
de Jonquierre transformation 289
Degenerary principle of Enriques 138
Degree of a curve 213
Degree of a polynomial 2
Degree of a rational map 143
Degree of an invertible sheaf 185
Degree of V 274
Derivation 189
Derivation, rule 189
Derived functions 221
Diagonal morphism 72 194
Difference kernel 74
Differential 189
Differential form 189 196
Differential form, rational 196
Differential form, regular 196
DIMENSION 22
Dimension of ringed space 42
Direct image sheaf 52 88
Direct sum 44 172
Discrete valuation 122
Discrete valuation ring 122
Divisor 125
Divisor defined by 125
Divisor defined by a section 154
Divisor group 125
Divisor, ample 156
Divisor, canonical 199
Divisor, effective 125
Divisor, exceptional 158
Divisor, horizontal 300
Divisor, locally principal 155
| Divisor, negative part of 125
Divisor, positive part of 125
Divisor, prime 124
Divisor, principal 125
Divisor, pull back of 130 132
Divisor, ramification 202
Divisor, reduced 257
Divisor, vertical 300
Divisor, very ample 156
Divisor, very ample, with simple normal crossings 257
Domain of rational function 79
Dominating 9 83
Dominating morphism 71
Dominating rational map 96
Dual curve 291
Dual homogeneous polynomial 291
Dynkin diagram 307
Dynkin type, reduced curve of 307 333
Easy addition theorem 303 310
Elliptic type 311
Embedded prime ideal 109
Enriques 138
Etale covering 248 338
Etale covering, endomorphism 336
Etale covering, map 30
Etale covering, morphism 248
Etale covering, space 30
Euclidean algorithm 5 286 288
Euler — Poincare characteristic 182
Exact presheaf 35
Exact sheaf 35
Exceptional divisor with respect to f 158
Extending base scheme 71
Extension theorem 124
Exterior power 194
f.g. type 84
Factorial ring 106
Fiber 73
Fiber type 312
Fiber, general 250
Fiber, generic 74
Fiber, product 70
Fibered variety 299 338
Fibered variety, canonical 311
Fibered variety, D-canonical 303
Fibered variety, proper 299
Fibered variety, proper smooth 299
Fibering theorem 302 310
Field of fractions 10
Field, residue class 12
Finite homomorphism 93
Finite morphism 92—93
Finite presentation 227
Finite type at a point 46—47
Finite type, of 85—86
Finitely generated graded algebra 162
Finitely generated graded ring 162
Finitely generated over R 162
Finiteness theorem 239 243
Fixed component 130
Fixed point 130
Flabby 177
Flex 244
Form, logarithmic 320
Form, rational 188
Form, regular 188 194
Fractions, module of 10
Free -module 44
Free A-module, graded 227
Fujita 211 318
Function field 95
Function field, rational 79
Fundamental sheaf 166
Gap sequence 219
General fiber 250
General member 250
General point 250
General type, of 311
Generator 46
Generic fiber 74
Generic point 15 34 74 83 291
Genus 208
Genus, arithmetic 182
Genus, formula of Clebsch 280
Genus, formula of Riemann 217
Genus, geometric 199
Genus, m 199
Genus, virtual 265
Geometric model 96
Germ 28
Glueing lemma 62
Glueing of morphisms 57
Graded A-module 160
Graded algebra, finitely generated 162
Graded free A-module 227
Graded R-algebra 160
Graded ring 160
Graph 72—73 76 133
Graph of rational map 133
Grothendieck 134 138 179 181 243
Group of numerical classes of divisors 266
Gutwirth 287
Hartogs 124
Height 23 107
hilbert 19 21 49 112 227 245
Hilbert nullstellensatz 19—20
Hironaka 255
Hirzebrush 182
Hodge's index theorem 267
Homogeneous coordinate system 63—64
Homogeneous element 160
Homogeneous ideal 160
Homogeneous spectrum 161
Homomorphism of presheaves 29
Homomorphism of sheaves 29
Homomorphism, 226—227
Homomorphism, 228—229
Homomorphism, canonical 10 34
Homomorphism, finite 93
Homomorphism, identity 29
Homomorphism, local 30 52
Hopf 295
Horizontal divisor 300
Hurwitz 216 224—225
Hyperbolic type, of 311
Hyperelliptic curve 217
Hyperplane section 150 214—215
Hypersurface 156
i 266
Ideals, sheaf of 59
Identity 29 52
Image, closed 83
Image, presheaf 33
Image, sheaf 33
Image, sheaf, direct 52 88
Immersion 61 71 77 93
Immersion, closed 61 71 76 86 89—91 93
Immersion, open 61 71 99
Index (D-) 220
Index of I 266
Index of speciality 212
Infinitely near points 278
Infinitely near singular point 279—280
Inflexion, point of 294
Initial form 118
Injective -module 174
Injective limit 28
Injective resolution 175
Injective sheaf 174
Injective theorem 175
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