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| Shafarevich I.R., Shokurov V.V., Danilov V.I. — Algebraic geometry I: Algebraic curves algebraic. Manifolds and schemes |
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| Предметный указатель |
 -Process 214
Abel mapping 157
Abel mapping, normalized 157
Abel, N.H. 29 41 73 139 154—158 161
Abelian variety 140 197
Abelian variety, principally polarized 148
Abstract vector 286
Adjunction 214
Affine line 285
Algebra of finite type 177
Algebra of finite type, flat 290
Algebra of finite type, integral 177
Algebraic group 139 196
Algebraic group, affine 180
Algebraic scheme 202 291
ample 262
Antiderivative 49
Artin, E. 197 293
Artin, M. 223
Arzela, C. 43
Atlas 188
Atlas, analytic 17
Atlas, complex 17
Atlas, equivalent 188
Automorphic form 74
Automorphic function 74
Automorphism 19 91
Babbage, D.W. 131
Base divisor 119
Base extension 193
Base point 119
Beltrami, E. 48
Belyi, G.V. 87
Bertini theorems 245 249
Bertini, E. 245 249
Betti, E. 41 230
Bezout theorem 109 111 251 273
Bezout, E. 109—111 133 251 252 255 273 281
Birationally equivalent 99
Bitangent, simple 137
Blow-up 214 216
Blowing-up 214
Bonnet, O. 73
Branch see also Ramification
Branch locus 31
Branch point 106
Brill, A. 123
Bundle see also Sheaf
Bundle, normal 207 208
Bundle, normal-cone 208
Bundle, tangent 208
Bundle, tautological 198
Bundle, universal 198
Bundle, vector 197
Bundle, vector, locally trivial 198
Bundle, vector, trivial 198
Canonical class 55
Canonical curve 117
Canonical divisor 54 108
Canonical linear system 120
Canonical map 81 117
Canonical model 85
Canonical polaxization divisor 160
Canonical region 67
Canonical sheaf 241
Cartesian square 193
Cartier, P. 255—257 260 267
Castelnuovo curve 126
Castelnuovo theorem 275
Castelnuovo, G. 89 126 127 129 275
Cauchy, A-L. 45
Cech, E. 84
Chart, affine 17 188
Chart, compatible 188
Chart, complex 16
Chart, complex, analytic 17
Chasles, M. 280
Chern, S.S. 147 270
Chevalley constructibility theorem 219
Chevalley semi-continuity theorem 228
Chevalley, C. 219 228
Chow ring 271 273
Chow variety 244 278
Chow's Lemma 86 145 223 224
Chow, W-L. 86 127 145 146 172 223 224 244 271—274 276 278
Clebsch, R.F.A. 89 135 137 138
Clifford's theorem 124 125
Clifford, W.K. 124 125
Coarse moduli space 78 117
Coclosure 58
Codimension 236
Cohen — Macaulay property 239
Cohen — Seidenberg theorems 221
Cohen, I.S. 221 238 239 243 273 290
Coherent sheaf 201
Collineation 195
Component, irreducible 211
Cone 190
Cone, normal 208
Cone, tangent 206
conic 21 94
Conormal set 246
Coordinates, affine 17
Coordinates, complex 16
Coordinates, conformal 48
Coordinates, homogeneous 187
Coordinates, isothermal 48
Coordinates, real 22
Correlation isomorphism 92
Correspondence 213
Cousin, P. 57
Covering, etale 233
Covering, n-sheeted 30
Covering, universal 30
Covering, unramified 30
Criterion for ampleness, Nakai — Moishezon 262
Criterion for separatedness 192
Criterion for simplicity, Jacobian 237 238
Cubic 94
Cubic curve 55
Cubic in Weierstrass normal form 88 151
Cubic plane 94
Curve, algebraic 94
Curve, algebraic plane, complex 20
Curve, algebraic plane, real 22
Curve, algebraic, complex 104
Curve, algebraic, irreducible 34
Curve, canonical 117
Curve, Castelnuovo 126
Curve, dual 136
Curve, elliptic 140
Curve, elliptic, complex 20
Curve, extremal 126
Curve, Fermat 21
Curve, hyperelliptic 101
Curve, linearly normal 120
Curve, m-normal 128
Curve, nondegenerate 120
Curve, nonsingular 20
Curve, plane 94
Curve, projectively normal 128
Curve, rational normal 121 195
Curve, space 94
Curve, strange 95
Curve, supersingular 149
Curve, trigonal 124
Cusp 134
Cycle, algebraic 266
Cycle, effective 266
Cycle, Schubert 269
| Danilov, V.I. 89 100 111
de Rham cohomology groups 47
de Rham theorem 51
Degeneration 207
Degree of a curve 109
Degree of a cycle 268 273
Degree of a divisor 28 107 259
Degree of a hypersurface 93
Degree of a linear system 119
Degree of a map 29 99 233
Degree of a variety 147 250
Degree, local 234
Descartes' folium 35
Descartes, R. 35
Desingularization 34 100
Development 37
Differential 45 208
Differential, closed 47
Differential, coclosed 58
Differential, cohomologically trivial 47
Differential, differentiable 45
Differential, exact 47
Differential, harmonic 58
Differential, holomorphic 52
Differential, meromorphic 54
Differential, of a function 102 204
Differential, of the first (second, third) kind 57
Differential, rational 102
Differential, regular 103
Differential, relative 293
Differentiation 44 102
Differentiation, universal 102
DIMENSION 93 226
Dimension of a chart 20
Dimension of a linear system 265
Dimension of a manifold 20
Dimension of a scheme 289
Dimension of a variety at a point 95 226
Dimension, real 22
Direct image of a cycle 266
Direct image of a sheaf 201
Direct sum of vector bundles 198
Dirichlet's principle 65
Dirichlet, P.G.L. 65
Divisor 27 107 244
Divisor of a fibre 28 107
Divisor of a function 28 107
Divisor of a meromorphic differential 54
Divisor of poles 28 108
Divisor of zeros 28 108
Divisor, ample 262
Divisor, base 119
Divisor, canonical 54 108
Divisor, Cartier 255
Divisor, effective 27 107 256
Divisor, finite 28
Divisor, group 27 107
Divisor, hyperplane section 109
Divisor, hypersurface section 109
Divisor, linearly equivalent 29 108 257
Divisor, local equation 255
Divisor, polarization 142 147 148
Divisor, polarization, canonical 160
Divisor, polarization, principal 148
Divisor, prime 108
Divisor, principal 28 108
Divisor, principally polarized 148
Divisor, special 123
Divisor, special, exceptional 123
Divisor, special, ordinary 123
Divisor, Weil 256
Domain of definition of a rational map 212
Domain of regularity 97 98
Dominant map 98 213
Double point 134
Double point, ordinary 134
Dual curve 136
Duality, Poincare 44
Duality, Serre 84
Elliptic curve 140
Elliptic curve, complex 20
Elliptic points 76
Elliptic transformation 76
Enriques, F. 131 226 247
Equivalence, algebraic, of cycles 267
Equivalence, linear, of divisors 29 108 257
Equivalence, rational, of cycles 267
Etale covering 233
Etale morphism 232 293
Euler characteristic 39
Euler, L. 39 56 64 72
Faltings, G. 87
Family of curves, algebraic 117
Family of cycles 267
Family of divisors 157 260
Family of divisors, algebraic 157
Family of Riemann surfaces 77
Fano, G. 132 265
Fermat curve 21
Fermat, P. de 14 21
Fibre of a morphism 182 192 288
Fibre product 193
Finite divisor 28
Finite mapping 29 107
Finite morphism 217 289
Form, automorphic 74
Form, differential 1- 45 208
Form, initial 206
Fourier, J. 145 146
Frobenius mapping 101 182
Frobenius, F.G. 101—103 106 142—144 182 197 204
Fubini, G. 48 69
Fubini-Study metric 48
Fuchsian group 75
Fulton, W. 248 249 251 271
Function, algebraic 21
Function, automorphic 74
Function, holomorphic 19
Function, meromorphic 23
Function, primitive 49
Function, rational 86 90 96 212
Function, regular 91 175 178
Function, regular, at a point 185
Fundamental class of a divisor 142
Fundamental group 30
Galois mapping 32 101
Galois, E. 32 38 39 101 103 233 281 286
Gauss mapping 247
Gauss, C.F. 20 24 36 49 68 69 73 76 211 247
Gaussian plane 20 68
Gel'fand, I.M. 177
Genus of a curve 112
Genus, arithmetic 84 255
Genus, geometric 52 53 135 241
Genus, topological, of a Riemann surface 38
Geometrization 291
Gluing 189
Graph of a morphism 181 193
Graph of a rational map 213
Grassmann variety 190
Grassmann, H. 94 190 195 196 198 207 208 244 245 258 259 266
Green, G. 50 52 57
Green, M. 132
Grothendieck, A. 225 230 240 294
Group of cycle classes 267
Group, additive 197
Group, multiplicative 197
Gysin homomorphism 272
Gysin, W. 270 272 273
Halphen, G.H. 127 128
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