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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)
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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Название: Algebraic Geometry II : Cohomology of Algebraic Varieties. Algebraic Surfaces (Encyclopaedia of Mathematical Sciences)

Авторы: Shafarevich I.R., Danilov V.I., Iskovskih V.A.

Аннотация:

This EMS volume consists of two parts. The first part is devoted to the exposition of the cohomology theory of algebraic varieties. The second part deals with algebraic surfaces. The authors have taken pains to present the material rigorously and coherently. The book contains numerous examples and insights on various topics.This book will be immensely useful to mathematicians and graduate students working in algebraic geometry, arithmetic algebraic geometry, complex analysis and related fields.The authors are well-known experts in the field and I.R. Shafarevich is also known for being the author of volume 11 of the Encyclopaedia.


Язык: en

Рубрика: Математика/Алгебра/Алгебраическая геометрия/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1995

Количество страниц: 262

Добавлена в каталог: 12.03.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$\mathbb{O}_l$-Sheaf      110
$\sigma$-Process      163
$\sigma$-Process in a point      163 165
$\zeta$-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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