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| Friedman R. — Algebraic Surfaces and Holomorphic Vector Bundles |
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| Предметный указатель |
 graph 81
lattice 81
 -map 205
 -Process 59
Abundance theorem 279 293 306
Ad V 99
Adjoint bundle see "ad V"
Adjunction formula 13
Albanese map 118 289
Albanese variety 288
Algebraic function field 271 275
Allowable 148
Almost decomposable 2
Ample cone 19
Andreotti, A. 278
Artin's criterion 75 80
Atiyah — Singer index theorem 207
Atiyah's theorem on vector bundles 1 33
Atiyah, M. 1
Auslander — Buchsbaum dimension formula 51 199
Barth, W. 3 162 310
Base point, assigned 69
Base point, infinitely near 69
Base point, simple 69
Base point, unassigned 69
Bauer, S. 240
Bloch, S. 312
Blowing down 66
Blowing up 59
Bogomolov number 274
Bogomolov — Miyaoka — Yau inequality 1 282
Bogomolov's inequality 3 22 107 149 163 245—247 305
Bogomolov, F. 3 245
Bombieri's theorem 79 248
Bombieri, E. 1 248
Botany 282
Brosius, J.E. 3 150 310
Brussee, R. 312
Canonical bundle formula 176
Canonical curve 134 139
Castelnuovo — deFranchis theorem 283 302
Castelnuovo's criterion 1 64—67
Castelnuovo's theorem 278
Catanese, F. 14
Cayley — Bacharach property 40 126
Chambers of type (w,p) 100
Chern class 27—30
Chern class, total 28
Chevalley, C. 275
Chow group 28 312
Chow's theorem 7
Class field theory 271
Class of type (w, p) 100
Classification of threefolds 305
Clifford's theorem 163 256
Compatible pair 186
Complex torus see "Torus"
Computation sequence 80 168
Connected, numerically 24 191
Connection 101
Connection matrix 102
Connection, anti-self-dual 105 206
Connection, flat 102
Connection, Hermitian 102
Connection, Hermitian — Einstein 3 104 245
Connection, integrable 102
Connection, irreducible 102
Connection, self-dual 105
Connection, unitary 102
Contraction 66
Cremona transformation 69
Curvature 102
Cusp 14 23 138 173
Deformation theory 155
Degree of a torsion free sheaf 198
Degree, normalized 85
Depth 51
Desale, U.V. 2
Descent theory 145 265
Destabilizing 86
Div X 9
Divisor 9
Divisor class 10
Divisor, big 20 72
Divisor, effective 9
Divisor, nef 20 72
Dolgachev, I. 189 278
Donaldson invariant 101 197 203 205
Donaldson polynomial 205
Donaldson polynomial on  206
Donaldson — Uhlenbeck — Yau theorem 106 245
Donaldson, S. 3 208 308
Double cover 2 46—50 57
Double point, ordinary 14 23 133 138 173 241
Double point, ordinary, threefold 210 242
Double point, rational 77—78 81—83 128 129 134 138 178 182
Dual complex 75
Dual graph 75 173
Dualizing sheaf 13
Dynkin diagram 173
Effective see "Divisor effective"
Elementary modification 41—42 55
Elementary transformation 114 118
Elimination of indeterminacy 68
Elliptic normal curve 128
Embedded resolution 63
Enriques' theorem 1 280
Enriques, F. 278
Enumerative geometry 2 3
Equivalence of families of vector bundles 153
Equivalence, linear 10
Equivalence, numerical 17
Euler characteristic 9
Euler characteristic, holomorphic 9
Euler exact sequence 109
Eventually base point free 21 72
Exceptional curve 66—67
Exceptional divisor 59
Expected dimension 158
Extended root system 173
Extremal rays 305
Factorization of birational morphisms 67
Faithfully fiat 275
Fernandez del Busto, G. 245
Fibration 167
Fintushel, R. 240
Formal functions theorem 62 65 74
Freedman, M. 278
Fulton, W. 4 28
Fundamental cycle 79—82 191
Galois cohomology 184 185
Galois morphism 272
General type see "Surface general 277
Generic rank 26
Genus drop 14
Genus drop, local 14
Genus, arithmetic 13
Genus, geometric 8
Geography 282
Geometric invariant theory 1 154
Gieseker compactification 206
Gieseker, D. 2 154 245 257 259 307 310
Goettsche, L. 206
Gomez, T. 311
Gomprecht, D. 313
Grauert's contraction theorem 72
Grauert, H. 72
Griffiths, P. 4
Grothendieck — Riemann — Roch theorem 4 29 48 212 213 215
Grothendieck's theorem on vector bundles 1 33
| Grothendieck, A. 1 154
Harder — Narasimhan filtration 97 112
Harris, J. 4
Hartogs' theorem 60 67
Hartshorne, R. 3 259
Hilbert scheme 155 164 204
Hirzebruch signature theorem 9 22
Hodge index theorem 9 16—18 23
Hodge theory 8—9 17
Homological invariant 186
Hoppe, H.-J. 3 310
Horikawa, E. 282
Hulek, K. 3 162 310
Infinitely near 63
Intersection pairing 8 11
Irregularity 8
Irregularity, birational invariance of 62 70
Italian algebraic geometry 1 278
J-function 185
Jordan — Hoelder filtration 112 154
Kahler identities 105 106
Kahler manifold 101 103
Kametani, Y. 218
Kawamata — Viehweg vanishing theorem 245
Klein, F. 83
Kobayashi — Hitchin conjecture 3
Kobayashi, S. 3 106
Kodaira classification 7
Kodaira classification of surfaces 278
Kodaira dimension 7 277
Kodaira dimension of the moduli space of bundles 311
Kodaira vanishing theorem 22 247
Kodaira — Spencer class 156
Kodaira, K. 1 70 131 175 176 186 187 189 249
Koszul complex 32
Kotschick, D. 278
Kronheimer. P. 3
Lang, S. 275
Leading coefficient of the Donaldson polynomial 240
Lefechetz theorem on (1,1)-classes 18
Lefechetz theorem on hyperplane sections 22
Leray spectral sequence 4
Leung, N. 3
Li, J. 207 308 310 311
Logarithmic transformation 187
Luebke, M. 3 106
Lueroth problem 287
m-sequence 51
Maruyama, M. 3 154 158 162 307 310
Matsumura, H. 4
Mayer, A. 135
Mehta, V.B. 246
Mehtar — Ramanathan restriction theorem 246 309
Minimal model 70—71
Minimal model of a threefold 306
Minimal model, relatively 171
Minimal model, strong 71—72
Miyaoka, Y. 245
Moduli functor 153
Moduli space 153
Moduli space, coarse 154
Moduli space, fine 155
Moishezon, B. 175 189 249
Monads 3
Monoidal transformation 59
Morgan, J.W. 207 240
Mori theory 4 277 279
Mori, S. 4 279 305
Mrowka, T. 3
Mukai, S. 3 310
Multiple fiber 169
Multiplicity 60
Multiplicity of a multiple fiber 169
Mumford's vanishing theorem 22 247
Mumford, D. 1 21 22 72 78 154 246 312
Nagata, M. 91
Nakai — Moishezon criterion 18—21 23
Narasimhan — Seshadri theorem 2 3 105
Narasimhan, M.S. 2 313
Nef, relatively 172
Noether's formula 9 22
Noether's inequality 281
Normalized degree 85
Num X 17
O'Grady, K. 240 310—311
Ogg, A. 194
Okonek, C. 278
Orbifold 188
Orbifold fundamental group 188
Oriented wall 100
Period map 133 297
Picard number 18
Pidstrigach, V. 278
Plurigenera 9
Plurigenera, birational invariance of 62 70
Poincare duality 8
Poincare line bundle 263
Principal homogeneous space 183
Projection formula 24
Projective dimension 51
Projective tangent cone 60
Projectively normal 128
Proper transform 60
Qin, Z. 163 278
Quot scheme 155
Ramanan, S. 2 313
Ramanathan, A. 246
Ramanujam's lemma 191
Rational equivalence 28
Rational normal curve 116
Rational surface singularity 74—78 80—82 138
Reflexive 45 53-54 56
Reider's theorem 249 274
Reider, I. 248
Relative duality 177
Relative Picard variety 263
Representable functor 153
Riemann — Roch theorem 4
Riemann — Roch theorem for a curve 4 30 57
Riemann — Roch theorem for a surface 4 9 15—16 23 30 57
S-equivalence 154
Sato, Y. 218
Schwarzenberger, R.L.E. 1 2 46 48 49
Segre — Nagata theorem 91 123
Segre, C. 91
Seiberg — Witten invariants 9 278
Seiberg, N. 9
Serre duality 16
Serre, J.-P. 37
Seshadri, C.S. 2
Shafarevich, I.R. 1 194
SIMPLE 2 88
Simpson, C. 154
Singular support 43
Slant product 205
Spindler, H. 3 310
Splitting principle 28
Stability, 2
Stability, Gieseker 2 3 96—97 154
Stability, Gieseker — Maruyama 2
Stability, Mumford — Takemoto 2 86
Stability, slope 2
Standard quadratic transformation 59
Stein factorization 21
Stein neighborhood 74
Stern, R. 240
Sub-line bundle 32
Suitable ample divisor 142
Support 43
Surface, abelian 132 137 293
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