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| IItaka S. — Algebraic Geometry: An Introduction to Birational Geometry of Algebraic Varieties |
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| Предметный указатель |
Integral affine scheme 51
Integral closure 102 140
Integral element 16
Integral extension 16 23
Integral morphism 89—91
Integral morphism, strictly 90
Integral over B 16—17
Integral scheme 56
Integrally closed 102
Intersection matrix 269
Intersection number 260—261
Intersection number, local 261
Inverse image  -ideal 147
Inverse image -module 145
Inverse image scheme 74
Inverse image sheaf 144
Inverse image, scheme theoretic 132
Invertible sheaf 150
Invertible sheaf, R-very 156
Invertible sheaf, very ample 156
Involution, canonical 224 271
Irreducible component 14—15 22
Irreducible decomposition 14
Irreducible element 105
Irreducible ideal 108
Irreducible space 14
Irregularity 199
Irregularity, logarithmic 325
Isolated point component 138
Jacobian 192
Jacobian matrix 192
Jacobson radical 20 111
Jung 287
K-valued point 69
K3 surface 306
Kawamata 314 342
Kernel 33
Kernel, difference 74
Kodaira 209 298
Kodaira dimension 298 309
Kodaira dimension, logarithmic 326
Krull 22 111 116 123
Kuramoto 344
L-normalization 140
Lasker's theorem 109
Leray 182—183
Limit, injective 28
Limit, inverse 112
Limit, projective 112
Linear pencil theorem 287
Linear system 128 158
Linear system, complete 127
Linear system, pullback of 158
Linear system, reduced 130
Linear transformation 289
Local coordinate system 195
Local homeomorphism 31
Local homomorphism 30 52
Local intersection number 261
Local ring 12
Local ring, complete 113
Local ringed space 41
Local tangent 286
localization 12
Locally factorial variety 131
Locally principal divisor 155
Locally projective morphism 169
Logarithmic canonical fibered variety 338
Logarithmic coordinate system 321
Logarithmic form 320
Logarithmic forms,  -module of 321
Logarithmic genus 324
Logarithmic geometric genus 325
Logarithmic irregularity 325
Logarithmic Kodaira dimension 326
Logarithmic M-form 321 323
Logarithmic M-genus 325
Logarithmic ramification divisor 333
Logarithmic ramification formula 333
M-form, logarithmic 321 323
m-genus 199
M-genus, logarithmic 325
Maehara 319
Mapping associated with  4
Maximal contact curve 284
Module of fraction 10
Module of regular forms 188—189 194
Module, graded 160
Module, injective 174
Module, inverse image 145
Module, quasi-coherent 45 146
Monoidal transformation 253—254
Morphism of affine schemes 53
Morphism of finite type 85—86 94
Morphism of local ringed space 52
Morphism of ringed space 52
Morphism of S-schemes 64
Morphism of schemes 55
Morphism projection 66
Morphism, affine 88 94 184
Morphism, closed 90
Morphism, composition of 52
Morphism, diagonal 72
Morphism, dominating 71
Morphism, etale 248
Morphism, finite 92
Morphism, glueing of 57
Morphism, immersion 61 71 86 94
Morphism, immersion, closed 61 71 76 86 91—92 94
Morphism, immersion, open 61 71 99
Morphism, integral 89—91 94
Morphism, locally projective 169
Morphism, projective 239—241
Morphism, proper 92 94
Morphism, quasi-compact 184
Morphism, restriction of 53
Morphism, S-product of 70
Morphism, separated 75 94
Morphism, smooth 249
Morphism, structure 65
Morphism, universally closed 90 94
Multiplicative subset 9 12 102
Multiplicity 113 120
Nagata 18 99 287
Nakai's criterion 274—276
Nakayama's lemma 111 194
Nilpotent element 6 100
Nilradical 6 60
Noether's normalization theorem 17 18
Noether, Max 141 264
Noetherian Induction 241
Noetherian scheme 56
Noetherian scheme, affine 50
Noetherian topological space 14 25
Nonsingular complete geometric model 141
Nonsingular model 255
Nonsingular point 120
Nonsingular reduction model 259
Nonsingular variety 120
Normal point 103
Normal ring 102
Normal scheme 103
Normalization 17 140—141
Nullstellensatz 13 19—20
Oka's theorem 50
Open base 6
Open base of etale space 31
Open immersion 61 71 99
Ordinary singular point 280
Parabolic type, of 311
| Pencil theorem 270
Picard group 151
Picard number 266
Pluecker relation 291 295
Poincare 182
Point of inflexion 294
Point, closed 15 20 84
Point, general 290
Point, generic 13 34 83
Point, infinitely near 278
Point, K-valued 69
Point, nonsingular 120
Point, normal 103
Point, ordinary singular 280
Point, ramification 217
Point, regular 120
Point, Weierstrass 219—220
Presheaf 27
Presheaf of sets 30
Presheaf, exact 35
Presheaf, image 33
Presheaf, quotient 34
Presheaf, tensor product 37
Primary ideal 108
Prime divisor 124
Prime element 1
Prime factor 106
PRODUCT 66—68 70
Product, fiber 70
Product, Segre 170
Projection 66
Projection, formula 146
Projective limit 112
Projective line 63
Projective morphism 239—241
Projective morphism, locally 169
Projective n-space 64 165
Projective scheme 165
Projective space 64 100 137 165 230
Projective variety 137 276
Projectively normal 246—247
Proper birational 136 324
Proper birational geometry 139
Proper birationally equivalent 137
Proper fibered variety 299
Proper morphism 92
Proper smooth fibered variety 299
Proper transform 143 256
Property  93
Puiseux expansion 297
Pullback 83
Pullback theorem 149
Quadric transformation 278
Quasi-coherent 45 146
Quasi-compact 13 15 184
Quasi-finiteness theorem 114
Quotient 10
Quotient field 10
Quotient presheaf 34
Quotient ring, total 10
Quotient sheaf 34
Radical 6
Radical, Jacobson 20
Ramification, divisor 202
Ramification, formula 202
Ramification, index 203
Ramification, point 217
Ramification, point, canonical 217
Rational function 79 152
Rational map 82
Rational map associated with linear system 128
Rational map, domain of 82
Rational map, graph of 133
Rational map, m-th canonical 200
Rational map, proper 136
Rational map, separable 198
Rational map, strictly 134—135
Rational section 152—153
Reduced affine scheme 51
Reduced divisor 257
Reduced divisor obtained from linear system 130
Reduced ring 50
Reduced scheme 50 60
Reducible curve of Dynkin type 307
Reducible element 105
Reducible ideal 108
Reduction model 134—135
Regular form 188 194
Regular function 78
Regular local ring 117 121
Regular point 120
Regular section 175
Regular system of parameters 117
Residue class field 12 155
Resolution, injective 175
Restriction map 27
Restriction of  28 59
Restriction of morphism 53
Restriction of rational map 83
Riemann 185 187 208 216
Riemann — Hurwitz formula 216
Riemann — Roch inequality 265
Riemann — Roch theorem 185 208 264—265
Riemann — Roch theorem for curve 208
Riemann — Roch theorem for surface 265
Riemann — Roch theorem, weak form 185 187
Ring 4
Ring of rational functions 79
Ring, Artinian 26
Ring, complete local 113
Ring, discrete valuation 122
Ring, graded 160
Ring, reduced 50
Ring, regular local 117
Ringed space 41 63
Ringed space, local 41
Ruled variety 309
S-morphism 64
S-product 66
S-product of morphisms 70
S-scheme 64 68—69
Samuel function 113
Scheme 54
Scheme, affine 41
Scheme, affine Noetherian 50
Scheme, base 65
Scheme, closure 92
Scheme, complete 92
Scheme, integral 56
Scheme, integral affine 51
Scheme, inverse image 74
Scheme, Noetherian 56
Scheme, normal 103
Scheme, projective 165
Scheme, reduced 56 60
Scheme, reduced affine 51
Scheme-theoretic intersection 62
Scheme-theoretic inverse image 132
Section 30—31
Section of etale space 30—31
Section of invertible sheaf 154
Section of sheaf 33
Section, hyperplane 156
Section, rational 152—153
Section, regular 152
Segre product 170
Seidenberg 23
Separable dominating rational map 198
Separated 78
Separated over Y 75—77 82
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