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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
Hopf, H.      88 239 241
Horroks, G.      46
Hypercohomology      22
Hyperelliptic surface      142
Illusie, L.      55 60
Image of a sheaf, direct      19 93
Image of a sheaf, inverse      19 93
Index of Del Pezzo surface      234
Inequality, Bogomolov — Miyaoka — Yau      292
Inequality, Castelnuovo — de Franchis      186
Inequality, Cauchy — Bunjakovski      85
Inequality, Noether      192
Inequality, Riemann — Roch      157
Infinitely near point      167
Inoue, M.      242
Intersection complete      135
Intersection number      151
Intersection number, local      151
Inverse image      19 93
Invertible sheaf      27
Irregularity      132
Jacobian      101
Jacobian family      206 241
Jacobian fibration      206
Kleiman, S.L.      163
Klein, F.      173 219
Kodaira dimension      133
Kodaira, K.      58 59 133 157 179 194 202 242
Koszul, J.-P.      2 29 32
Kummer surface      141
Kummer, E.      4 91 96 98—101 225
Kunneth, H.      2 5 17 29 32 59 110 141
l-adic cohomology      109
l-adic cohomology, Betti number      110
l-adic sheaf      109
l-adic sheaf, locally constant      109
l-adic sheaf-lisse      109
L-function      113
La Vallee Poussin, C.      117
Lattice      160
Laurent, P.A.      67
Lefschetz, S.      3 5 41 65—68 76 108 112 113 118 129 148 149 243 247
Lemma on an equivalent complex      42
Lemma on residues      50
Leray, J.      10 24 31 96
Lie, S.      223
Linear system      144
Linear system, complete      144
Linearly equivalent divisors      147
Liouville, J.      190
Lisse l-adic sheaf      109
Lobachevski, N.I.      219 225
Local equation      143
Local intersection number      151
Localization, strict      94
Locally acyclic morphism      107
Locally constant l-adic sheaf      105
Locally constant sheaf      18
Luroth, J.      129—131 231 247 248
Macaulay, F.S.      3 30 53
MacPherson, R.      65
Marked K3, surface      224
Mathieu, E.L.      226
Mayer, W.      24 73
Microweight      235
Minimal model      175
Minimal resolution      173
Minkowski, H.      92
Mixed sheaf      120
Miyaoka, Y.      191
Model, canonical      185
Model, Cayley — Klein      219
Model, minimal      175
Model, Neron      199
Model, relatively minimal      181
Model, smooth      174
Moishezon, E.G.      161 185
monodromy      74 108
Monoidal transformation      163
Moore, J.      3 63
Mordell, L.J.      6 197
Mori, S.      163 182
Morphism etale      87
Morphism of complexes      12
Morphism, Frobenius      56
Morphism, locally acyclic      107
Morse, M.      243
Mumford, D.      36 46 186 195
N-genus      133
Nakai, Y.      161 185
Nakano, S.      58
Nef      175
Neighborhood etale      94
Neron, A.      71 145 163
Noether, M.      20 130 132 156 170 179 192 212 219 233 249
Non-classical bi-elliptic surface      249
Non-classical Enriques surface      249
Nonsingular model      174
Normal bundle      154
Normal form Weiterstrass      197
Number of fixed points      65
Number, Betti k-th      63
Number, Betti k-th, l-adic      110
Number, Hodge      11 54
Number, Picard      145
Number, pure      115
Numerically effective class      175
Numerically effective divisor      175
Numerically equivalent divisors      156
Operator boundary      8 12
Operator, Cartier      57
Operator, coboundary      9 96
Order of an infinitely near point      167
Orientation sheaf      111
Path      106
Pencil Halphen      210
Pencil of curves      133
Period of a surface      222
Picard, E.      92 98 108 127 145—149 158 174 192 207 212 219 224 233 246 249
Plane fake      195
Plurigenus      133
Poincare, H.      6 7 50 59 65 71 111 130 148 151
Point of indeterminacy      167
Point, Du Val singular      173 203
Point, geometric      94
Point, infinitely near      167
Point, singular rational double      173
Polarized surface      215
Polynomial Frobenius characteristic      116
Polynomial, Hilbert      38
Positive half      159
Presheaf      17
Presheaf, etale      91
Primary Hopf surface      239
Primitive vector      224
Principal divisor      143
Principally polarized surface      215
Principle A-covering      97
Principle homogeneous space      206
Problem Luroth      230
Problem, rationality      133
Problem, Riemann      37 44
Problem, Riemann, general      44
Problem, Schottky      150
Proper transform of a curve      164
Pure number      115
Pure sheaf      115
Pure sheaf of weight r      115
Pure weight      72 115
Quadric      134
Quadric fake      195
Quasi-algebraically closed field      82
Quasi-coherent sheaf      31
Quasi-elliptic fibration      245
Quasi-elliptic surface      245
Quasi-isomorphism      12
Quotient variety      136
Ramanujam, C.P.      157
Rational double point      173
Rational family      147
Rational ruled surface      138 231
Rationally equivalent divisors      147
Raynaud, M.      248
Rees, D.      41
Reflection      219
Regular sequence      30
Regular sheaf      36
Relatively minimal model      181
Relatively numerically effective divisor      181
Remrnert, R.      70
Representable functor      91
Resolution Godemant      21
Resolution minimal      173
Resolution of a complex      13
Resolution of a sheaf      10
Resolution-flabby      21
Restriction      17
Riemann problem      27 44
Riemann — Roch theorem for curves      44
Riemann, B.      2 3 6 27 40 44 70 85 116 127 132 140 156
Ring Chow      45
Ring, Cohen — Macaulay      30
Ring, Gauss      88
Ring, Hensel      94
Roch, G.      2 3 49 127 132 140 156
Rokhlin, V.A.      211
Root      204
Ruled surface      138 226 237
Sard, A.      137
Scheme, Cohen — Macaulay      30
Scheme, Hensel      94
Scheme, simply connected      88
Schottky, F.      150
Schwarzenberger, R.L.E.      47
Section global      17
Section global of a presheaf      17
Sections compatible      18
Seifert, H.K.L.      201
Semisimple sheaf      118
Sequence exact      11
Sequence of complexes      13
Sequence, Euler      35
Sequence, exponential      70 147
Sequence, Hodge — de Rham spectral      54
Sequence, Kummer      96
Sequence, Leray spectral      24 96
Sequence, Mayer — Vietoris      24
Sequence, regular      30
Sequence, spectral      14
Serre, J.-P.      2 6 28 50 58 67 86
Severi, F.      71 130 145 163 215
Sheaf      9 18 92
Sheaf of $\mathbb{Z}_l$-modules      109
Sheaf of weight r      115
Sheaf, abelian      19 95
Sheaf, acyclic      10
Sheaf, coherent      35
Sheaf, constant      18
Sheaf, constructible      103
Sheaf, dualizing      53
Sheaf, etale      92
Sheaf, flabby      20
Sheaf, flat      32
Sheaf, invertible      27
Sheaf, l-adic      109
Sheaf, lisse      109
Sheaf, locally constant      109
Sheaf, mixed      116
Sheaf, orientation      111
Sheaf, pure      115
Sheaf, pure of weight r      115
Sheaf, quasi-coherent      27
Sheaf, regular      36
Sheaf, semisimple      118
Signature of a surface      193
Simple singularity      173
Simplex singular      9
Simply connected scheme      88
Singular cohomology      63
Singular homology      63
Singular point rational double      173
Singular point, Du Val      173 203
Singular simplex      9
Singularity canonical      173
Singularity, Du Val      173
Singularity, Klein      173
Singularity, simple      173
Space principle homogeneous      206
Space, Teichmuller      190
Specialization      106 107
Spectral sequence      14
Spectral sequence, degenerates      55
Spectral sequence, Hodge — de Rham      54
Spectral sequence, Leray      24 96
Stable bundle      237
Stable fiber      224
Stable surface      237
Stalk of a sheaf      19 94
Stein factorization      137
Stein, K.      72 108 137 187—188
Stiefel, E.      221
Strict localization      94
Supersingular curve      84
Supersingular surface      247
Surface of general type      136 183
Surface of type VII      242
Surface, abelian      214
Surface, algebraic      131
Surface, bi-elliptic      142 183 217
Surface, bi-elliptic, classical      249
Surface, bi-elliptic, non-classical      249
Surface, complex      237
Surface, Del Pezzo      232
Surface, elliptic      139 196 241
Surface, Enriques      142 183 212
Surface, Enriques, classical      249
Surface, Enriques, non-classical      249
Surface, Fermat      146 153 248
Surface, Godeaux      136
Surface, Hopf      239
Surface, hyperelliptic      142
Surface, Inoue      242
Surface, K3      141 219
Surface, K3, marked      224
Surface, Kodaira      194 242
Surface, Kummer      141
Surface, polarized      215
Surface, principally polarized      245
Surface, quasi-elliptic      245
Surface, rational ruled      138 231
Surface, ruled      138 226 237
Surface, stable      237
Surface, supersingular      247
Surface, Veronese      232
Symplectic algebraic variety      226
Symplectic automorphism      226
System without fixed components      144
System, linear      144
Tate, J.T.      5 100 120
Teichmuller, O.      190
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