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| Shafarevich I.R., Danilov V.I., Iskovskih V.A. — Algebraic Geometry II : Cohomology of Algebraic Varieties. Algebraic Surfaces (Encyclopaedia of Mathematical Sciences) |
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| Предметный указатель |
 -Sheaf 110
 -Process 163
-Process in a point 163 165
 -function 83
(-1)-Curve 171
(-2)-curve 173 219
A-Covering principal 97
A-Torsor 97
Abelian sheaf 19 95
Abelian surface 214
Abelian surface, variety 140
Acyclic complex 12
Acyclic complex, covering 25
Acyclic complex, sheaf 10
Albanese map 180
Albanese, G. 127 149 180 188 209 249
Algebraic family 145
Algebraic family, fundamental group 89
Algebraic family, surface 131
Ample element 146
Analytification 61 67
Arithmetic genus 132
Artin, E. 41 83 85
Artin, M. 76 104
Autoduality 106
Automorphism symplectic 226
Base 137
Beauville, A. 142
Bertini, E. 50 137 244 245
Betti, E. 6 63 110 119 152 243
Bezout, E. 152
Bi-elliptic surface 142 183 217
Bi-elliptic surface, classical 249
Bi-elliptic surface, non-classical 249
Bicomplex 15
Blowing up 163
Bogomolov, F.A. 191
Borel, A. 3 63
Boundary of a symplex 8
Boundary of a symplex, operator 8 12
Brauer, R.D. 208
Bunjakovski, V.J. 85
Calabi, E. 193
Canonical class 132
Canonical model 185
Canonical model, dimension 133
Canonical model, singularity 173
Cartan domain of type IV 223
Cartan, E. 194 223
Cartan, H. 6 28 67
Cartier, P. 18 57 71 105
Castelrmovo, G. 6 36 128 171 172 186 230
Category derived 12
Cauchy, A.L. 85
Cayley, A. 219
Chain of triangulation 8
Chain of triangulation, k-dimensional 8
Character Chern 46
Characteristic Euler 27 37 44 137 156
Chern, S.-S. 45 46 48 71 148
Chevalley, C. 60 81
Chow, W.L. 38 45 69 104
Class canonical 132
Class canonical of a subvariety 112
Class canonical of a surface 219
Class canonical, Chern 45 71
Class canonical, fundamental 64 111
Class canonical, numerically effective 171
Class canonical, Todd 46
Class canonical, total Chern 45
Classical bi-elliptic surface 249
Classical bi-elliptic surface, Enriques surface 249
Clebsch, A. 130
Clifford, W.K. 192
Coboundary 96
Cochain 9
Cochain complex 9
Cohen, D.E. 3 30 53
Coherent sheaf 35
Cohomology 9
Cohomology of a complex 12
Cohomology of a covering 25
Cohomology of a pair 13
Cohomology of a sheaf 10 21
Cohomology of a space 21
Cohomology with compact support 102 105
Cohomology, crystalline 59
Cohomology, de Rham 54 59 68
Cohomology, Galois 79 96
Cohomology, singular 63
Cohomology, Weil 86
Cohomology, Z-adic 86 109
Compatible sections 18
Complete linear system 144
Complete linear system, intersection 135
Complex of a covering 25
Complex surface 237
Complex, acyclic 12
Complex, chain 8
Complex, cochain 9 12
Complex, de Rham 54 68
Complex, filtered 13
Complex, Koszul 29
Complex, total 15
Components of weight r 72
Cone Mori 163
Cone Mori of a morphism 16
Conjecture Artin 83
Conjecture Artin, Grothendieck 120
Conjecture Artin, Hodge 120
Conjecture Artin, Mordell 6
Conjecture Artin, Riemann 83
Conjecture Artin, Tate 120
Conjecture Artin, Weil 7 85 115 116
Constant sheaf 18
Constructible sheaf 103
Covering acyclic 25
Covering acyclic, etale 87
Covering acyclic, F-acyclic 25
Covering acyclic, Galois 89
Covering acyclic, universal 89
Criterion acyclicity of a covering 26
Criterion acyclicity of a covering, Castelnuovo — Enriques contractibility 171
Criterion acyclicity of a covering, Castelnuovo — Enriques rationality 230
Criterion acyclicity of a covering, Kleiman ampleness 163
Criterion acyclicity of a covering, Nakai — Moishezon ampleness 161
Crystalline cohomology 59
Cubic 135
Curve 143
Curve, exceptional 153 176
Curve, exceptional of the first kind 171
Curve, supersingular 84
CYCLE 7
Cycle, vanishing 107
Danilov, V.I. 131
de Franchis 6 128 186
de Rham, G. 3 23 54 56 59 68 137
Deformation 242
Degenerate fiber 137 200
Degenerates spectral suquence 55
Degree of a curve 143
Degree of a curve of a polarization 215
Degree of a curve of a surface 153
Degree of a curve of Del Pezzo surface 233
Del Pezzo, P. 129 231—233
Deligne, P. 5 55 67 71 74 115 116 118
Depth of a local ring 30
Derived category 12
Differential 12
Dilatation 163
| Dimension canonical 133
Dimension canonical, Kodaira 133
Direct image 19 93
Divisor 143
Divisor of a function 143
Divisor, algebraically equivalent to zero 145
Divisor, effective 143
Divisor, linearly equivalent to zero 147
Divisor, nef 175
Divisor, numerically effective 175
Divisor, principal 143
Divisor, rationally equivalence to zero 147
Divisor, relatively numerically effective 181
Divisors equivalent 143
Divisors equivalent in general position 151
Divisors equivalent, linearly equivalent 147
Divisors equivalent, numerically equivalent 156
Divisors equivalent, rationally equivalent 147
Donaldson, S.K. 211
Du Val, P. 110 173 184 191 203 220 223
Duality Poincare 59 110 111
Duality Poincare, Poincare — Lefschetz 65
Duality Poincare, Serre 50 52
Dualizing sheaf 53
Dummy filtration 14
Effective divisor 143
Element ample 146
Element ample, very ample 146
Elementary transformation 172 229
Elliptic pencil 138
Elliptic pencil, surface 139
Enriques, F. 128 142 171 183 187 210—214 246—248
Equation local 143
Equivalent divisors 143
Etale covering 87
Etale covering, morphism 87
Etale covering, neighborhood 94
Etale covering, presheaf 91
Etale covering, sheaf 92
Etale covering, surjective 92
Euler characteristic 27 37 44 132 137 156
Euler, L. 35 37 43
Exact sequence 11
Exact sequence of complexes 13
Exceptional curve 153 176
Exceptional curve of the first kind 171
Exceptional vector 176
Exponential sequence 70 147
F-Acyclic covering 25
Fake plane 195
Fake quadric 195
Faltings, G. 6
Family algebraic 145
Family Jacobian 206 241
Family rational 147
Fano, G. 231
fe-Dimensional chain of a triangulation 8
fe-th Betti number 63
Fermat, P. 146 153 248
Fiber 137
Fiber, degenerate 137 200
Fiber, multiple 197
Fiber, stable 204
Fibration in curves 137
Fibration quasi-elliptic 245
Fibration, jacobian 206
Fibration, Seifert 201
Field quasi-algebraically closed 82
Filtered complex 13
Filtration 13
Filtration, dummy 14
Filtration, final 15
Filtration, Hodge 54
Filtration, weight 71
Final filtration 15
Fixed part 144
Flabby resolution of Godement 21
Flabby resolution of Godement, sheaf 20
Flat sheaf 32
Formula adjunction 154
Formula, Hirzebruch 48
Formula, Kunneth 17 32 59 66 110
Formula, Lefschetz 66 113
Formula, Leftschetz trace 113
Formula, Leftschetz, generalized 114
Formula, Noether 156
Formula, projection 112 153
Formula, Riemann — Roch 49
Formula, universal coefficients 110
Formula, Whitney 45
Freedman, M.H. 211
Frobenius action 60
Frobenius endomorphism 56 80 113
Frobenius, F. 56 80 115 244
Functor representable 91
Fundamental class 64 111
Fundamental group 88 89
Fundamental weight 235
Future tube 223
GAGA 67
Galois, E. 78 79 89 96 114 209
Gauss, C.F. 88
General Riemann problem 44
Generalized trace formula 114
Genus arithmetic 132
Genus geometric 130 132
Genus of a curve 6 28
Genus of a pencil 137
Geography of surfaces 192
Geometric genus 130 132
Geometric point 94
Global sections 17
Global sections, fundamental 89
Godeaux, L. 136 230
Godement, R. 23 96
Goresky, M. 65
Gram, J.P. 221 224
Grassmann, H. 64
Grauert, H. 68 70
Grothendieck, A. 3 4 7 38 39 48 59 68 75 104 114 120
Group algebraic, Brauer 208
Group algebraic, cohomology 8
Group algebraic, fundamental 88 89
Group algebraic, Neron — Severi 71 154
Group algebraic, Picard 147
Group algebraic, Poincare 54
Group algebraic, Severi 154
Group algebraic, Weyl 234
Gysin homomorphism 112
Gysin, W. 5 112
Hadamard, J. 117
half 159
Half, positive 159
Halphen, E. 210
Hard Lefschetz theorem 118
Hensel ring 94
Hensel scheme 94
Hensel, K. 98 113
Hilbert, D. 38 44 98 198
Hironaka, H. 62 70
Hirzebruch, F. 2 11 45 47 194
Hodge, W.V.D. 3 51 54 55 147 195 221 239 240
Holomorphic Poincare lemma 54
Homogeneous space principal 206
Homological equivalence 12
Homology 7
Homology of a complex 8
Homology of a triangulation 8
Homology, Borel — Moore 63
Homology, singular 8 9 63
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