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| Friedman R., Morgan J.W. — Smooth four-manifolds and complex surfaces |
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| Предметный указатель |
Donaldson's theorem on connected sums 425
Donaldson's theorem on definite 4-manifolds 3 425
Donaldson's theorem on diffeomorphisms of a K3 surface 194 408
Donaldson's theorem on stable bundles and ASD connections 4 279 323 324
Donaldson's theorem on the dimension of the moduli space 339 372
Donaldson's theorem on the failure of the h-cobordism theorem 3 4
Donaldson's theorem on the nonvanishing of the polynomial invariants of an algebraic surface 4 279 340 356—373 409
Donaldson's theorem on the orientation of the moduli space 329
Donaldson's theorem on the polynomial invariant of a blowup 411
Douady, A. 297 308
Dynkin diagram 179 181 183 184 187—192 401 403
Ebeling's theorem 8 191 192 194 405
Ebeling, W. 403 410
Eichler — Siegel transformations 399 404 405
Elementary equivalence 172 175—179
Elementary transformation of a family of vanishing arcs 168 169 171
Elementary transformation of a ruled surface 28
Elliptic fibration 7 23
Elliptic regularity 237 242 256
Elliptic structure 23
Elliptic surface 4 7 23 34—68 75—132
Elliptic surface with a section 34 56—68
Elliptic surface with Euler number zero 123—127 154
Elliptic surface with multiple fibers 35 48—51 95—110
Elliptic surface with positive Euler number 122 123
Elliptic surface without multiple fibers 75—95
Elliptic surface,  - 7 138 139
Elliptic surface, -, basic 196 202 212
Elliptic surface, -isomorphism of 138—140
Elliptic surface, algebraic 5 6 86 87 106 107 156
Elliptic surface, basic 16 45—48 56 75 82 85 89 93 95 96 98 102—109 113 123—125 127 142 159 196 202 203 442
Elliptic surface, deformation equivalence of 35 110—134
Elliptic surface, diffeomorphism classification of 5
Elliptic surface, Donaldson polynomials of 476 491 497
Elliptic surface, family of 35
Elliptic surface, isomorphism of 34
Elliptic surface, nodal 63 141
Elliptic surface, properly 23
Elliptic surface, rational 51 80 131 132 164 181—189 420 493
Elliptic surface, relatively minimal 23 34 51 56
Elliptic surface, ruled 51 131 132 199 209 217 222 224 420 492—495
Enriques — Kodaira classification 2 14—27
Equivalence of families of bundles 303
Equivalence of quadruples 126 202 206—208
Equivalence, oriented, of quadruples 126 127 202 206—208
Euler class 7 89 124
Euler number of an orbifold 146
Exceptional classes 411—416 419 421 425 426 428
Exceptional curve 16 17 21 23 24 28 154 155 394 491 493 494 497
Exceptional curve, stability of 24
Expected dimension 302 325 340 349 461
Extended G-equivalence 361—363
Family of elliptic surfaces 35
Family of surfaces 17
Family of vector bundles 303
Fiber connected sum 138 161 162 164 165 170 189 190 195 493 497
Flat base change 462 465 466 482 483 488
Foliation, complex 308—311
Formal orientation 330 355
Fr(M), the principal SO(4) bundle induced by the tangent bundle of M 251
Fractional linear transformation 36
Fredholm 235 290—292 294—296 328 352 355 385
Freed — Uhlenbeck theorem see "Generic metrics theorem"
Freedman, M. 3 31 161 410 496
Frobenius theorem 308 312 313
Functional (j)-invariant 43
Functional invariant 76
Fundamental group of an elliptic surface 157—159 198—201
G-linearization 362 365
Gauge group 3 231
Gauge group, based 233 330
Gauge group, complex 280 285 300
Gauge transformation, group of see "Gauge group"
Generic branching behavior 63—68
Generic metrics theorem 237 280 339
Geography 23
Geometric genus 18
Geometric invariant theory 334 337—339 357 359 362
Geometric representatives for the  -map 234 235 268—270 340 341 374 428—431 433
Gieseker compactification 339
Gieseker, D. 334 337—339 357 364 373
GIT (geometric invariant theory) 363
Griffiths, P. 282
Grothendieck — Riemann — Roch theorem 342 343 488
Grothendieck, A. 336 338 374
h-cobordism theorem 1 3 4 137
Hambleton, I. 136 137
Harvey, R. 201
Hermitian holomorphic vector bundle 281 323
Hilbert scheme 33
Hodge *-operator 12 236 294 319
Hodge decomposition 319
Hodge metric 9 323 324 338 339 341 346 352 353 369 379
Hodge structure 42 86 87 106
Hodge theory 2 6 86 87 91 92 294 323
Homogeneous polynomial, bounded, on a Banach space see "Bounded homogeneous polynomial"
Homological invariant 16 43 45 61 76 88 93 210
Hopf surface, primary see "Surface Hopf"
Hopf surface, secondary see "Surface Hopf"
Horizontal lift of a vector field 282 332
II*, a Kodaira fiber 181
III(B), the set of all algebraic surfaces in  86
Iitaka, S. 20 21 224
Index theorem, Atiyah — Singer 237 343
Index theorem, Hirzebruch 30
Index theorem, Hodge 19 367 373 406 446 454
Integrable (0,1)-connection see "Connection (0
Itoh, M. 332
J(C), the Jacobian of the algebraic curve C 345
J(S), the Jacobian (or basic) elliptic surface associated to the elliptic surface S 46
J,  43
j, the function induced by  on the quotient of the upper half plane by  37
J-invariant 16 43 44 47 56 58 60—68 84 113 121
j-invariant, constant 56 60—63 84 88 92 157
Jacobian surface J(S) 46 47 75 76 86 100 114 442 443 447 453
Jacobian variety 130 345 444 458
Kaehler identities 325 326
Kato's inequality 243
Kneser, M. 192 194
Knudsen — Mumford determinant 374
Kobayashi, S. 323
Kodaira dimension 4 7 14—16 19—31 50 51 128 130—132 155 156 221 223—225 394 494 498
Kodaira — Spencer complex 293 324
Kodaira — Spencer theory 6 9 279—280 390
Kodaira, K. 2 3 7 14 20 21 24 32—34 43 46 52 57 60 75 76 81—84 86 93—95 101 103 111 129 132—134 181 221 495
Koszul — Malgrange theorem 282
Kotschick, D. 498
Kreck, M. 497
Kronheimer, P. 497 498
Kuranishi map 295 297—299 301 305 327 328 355
Kuranishi model 293—303 305 314 319 327—329 335—337 355
Kuranishi obstruction map see "Kuranishi map"
Kuranishi's theorem 9 279 305—318 331
Kuranishi, M. 279 280
Lawson, B. 201
Leading coefficient 442 444 476 491 497
Lens space 133 136 137
Leray spectral sequence 48 79 80 83 86 87 89 90 93 110 121 122 201 265 449 463 464 473 474 482 483
Li, J. 339
Libgober, A. 410
Livne's theorem 8 139 172—179
Local complete intersection 350
Local complete intersection, moduli space is a 302
Local monodromy 44 45
Locally semiuniversal 305
Logarithmic transform 7 16 91 95—113 122—127 165 170 200—204 442 493
Logarithmic transform, - 138 143—145 196 197 202—204 210 212 213
Long vector 180 188
Luebke, M. 33 323 495
M,  , deformation functors for stable or semistable bundles on C 356 357
| Maier, F. 33 495
Manifold point 49
Maruyama, M. 338
Matsumoto, Y. 164 172
Maurer — Cartan form 280
Milnor number of a cusp 183
Minimal 4-manifold 419
Minimal complex surface 17—20 22 23 25—27 31—33 155 394
Minimal model of a 4-manifold 10 415—420 492
Minimal model of a complex surface 16 21 22 24 27 156 420 492
Minimal, strongly 419 420 492 494 499
Miniversal 305
Miyaoka, Y. 201
Moduli functor 342—344 357 364
Moduli functor, based 336 337
Moduli functor, global 280 303 304 334—336
Moduli functor, local 9 279 280 304 305 337
Moduli functor, rigidified 363 364
Moduli space, based 237 246 330 331 336 337 342 344 379
Moduli space, coarse 57 63 280 335 337 338 357 364 368
Moduli space, fine 335
Moduli space, local 279 305
Moishezon, B. 33 56 64 66 111 113 122 138 158 164 169 172 196 409 410
Monodromy group 18
Mordell — Weil group 46 109
Morphism from a complex space to a Banach space 287 288
Mrowka, T. 497 498
Multiple fiber 16 35 95—120 125—127
Multiple fiber with singular reduction 35 96—100 113—122
Multiple points 49
Multiplicity of a multiple fiber 15 35 49 50
Multiplicity of a point of an orbifold 15 49
Multiplicity of an irreducible component of a complex space 349 350 353 355
Multisection 34 46 444 446 454 478
Mumford, D. 344 357 359 382
Nakai — Moishezon criterion 446
Narasimhan — Seshadri theorem 324 365 366
Negative definite 4-manifold 10 276 356 394 425 426 428
Newlander — Nirenberg theorem 283
Newlander — Nirenberg theorem, parametrized version 312
Newlander — Nirenberg theorem, real analytic case 308 311 312
Nodal see "Elliptic surface nodal"
Noether's formula 2 19 30
Normalized degree 321 323
O'Grady, K. 491 499
Obstruction bundle 247
Obstruction space 302 324 355
Ogg, A. 106
Okonek, C. 33 403 495
One-parameter subgroup criterion 359
Orbifold covering 145 146 149 156 198
Orbifold fundamental group 107 145—154 158 198 493
Orbifold map 146—154 153
Orbifold, bad 146 198 199 210
Orbifold, base, of an elliptic surface 7 15 49 51 105 111 122 125—127 131 132 138 146 154—158 198—202 205 207—220 224 409 492 493
Orbifold, flat 51 146 154—156 198 210 211 214—216 492 493
Orbifold, good 146—154 198
Orbifold, hyperbolic 51 146 154—156 198 210 211 213 492—493
Orbifold, spherical 51 128 146 198 210 216—220
Orientation of the moduli space 227 238 260 329 330 341 354
Orientation, formal 330 355
Oriented ordered basis 36—38
Pair of pants 149 150 151
Period matrix 345
Permissible representation 68 70
Permissible sequence 69 70
Pic X, the Picard group of X 11
Picard — Lefschetz formula 55
Pidstrigach, V. 498
Plurigenus 2 4 10 11 18 24—27 50 128 129 498 499
Poincare bundle 331—333
Poincare conjecture 1 2
Poincare line bundle 449—452 459 460 483 487 489
Poincare line bundle, first Chern class of 489
Poincare line bundle, relative 451 452
Polarization map 396
Pontrjagin square 233
Primary Hopf surface see "Surface Hopf"
Properly elliptic see "Elliptic surface properly"
q(S), the irregularity  19
Qin, Z. 31 498
Quadratic term of the Kuranishi map 299 300
Quillen, D. 374
Quot scheme 338
Reduced expression 172—174
Reflection 139 152 185 186 191—195 401—406 411 418
Reflection group 179 185 189 191—195 401—405
Relatively minimal see "Elliptic surface relatively
Removable singularity theorem see "Uhlenbeck's removable singularity theorem"
Representable functor 304 305 334 336
Ruling 20 28 59 443
S*V, the invariants of the symmetric group acting on the tensor algebra 395
Salvetti, M. 410
Schwarzenberger, R.L.E. 488
Secondary Hopf surface see "Surface Hopf"
Seifert fiber 7
Seiler's theorem 7 16 66—75 82 165
Seiler, W. 56 57 64
Self-dual 2-form 12 242 255 256 319
Self-dual curvature 247 254 255 327
Semistable bundle 323 356 359—361 365 366 373
Semistable point 359 360 362 363
Semistable torsion free sheaf 339
Semiuniversal see "Locally semiuniversal"
Seshadri, C. 357
Shafarevich, I. 2 14 16 19 75 84—86 106
Shioda, T. 87
Simple (0,1)-connection or vector bundle 283 294 296 300 302—305 314 323 325 327 336
Simultaneous resolution of double points 33 59 94 115 164
Singular support 244—246 248 249 251 254 257 263 266 347
Slice 231 232 294—297 306 308 326—331
slope 321
Smale, S. 1 3
Smooth divisor 268
SO(V,q), SO(V), the group of linear maps of V preserving the quadratic form q 397
SO(V,q;k), SO(V,k), the subgroup of SO(V q) fixing k 397
Sobolev completion 227 230 293 294 365 386
Sobolev embedding theorem 244
Sobolev multiplication theorem 241 293
Spin structure on a manifold 375—379
Spin(V) 375
Spin(V), the spin group associated to the quadratic form on V 375
Spinor norm, real 191 393 397 408 411 412 414 426
Spinors 235 268 375
Stable bundle 6 9 10 279 300 303 304 320—323 328—330 334—338 341 342 344 366 370
Stable bundles over curves 356—366
Stable elements 229 271—273 276 277
Stable point 360 361
Stable range 9 346 352 368 373 428
Stable submanifold 111 129
Stratification, local 247—260
Strongly minimal 4-manifold 419 420 499
Strongly minimal model 419
Sub-line bundle 321 367 445 450 453
Surface of type VII 5 14 156 157 221
Surface, Barlow 31 498
Surface, Dolgachev 31
Surface, Enriques 22 23 31—33 50 51 131 224 225 495
Surface, general type 4 7 23 24 28 29 31 33 155 221 409 410 494 498 499
Surface, geometrically ruled 20 28 29
Surface, Hopf 5 7 17 20 51 111 132—137 157 199 209 221 222 224 492 494 495
Surface, Hopf, primary 133—135 137
Surface, Hopf, secondary 133—135 209
Surface, hyperelliptic 22 23 31 32 50 51 130 131 214 215
Surface, Inoue 5 20 157
Surface, K3 3 4 22 23 31—33 50 51 131 132 194 224 225 408 416 442 490 491 494—497
Surface, Kodaira 22 23 32 33 50 130 131 214—216
Surface, rational 28 31 221 225
Surface, rational ruled 18 443 444
Surface, ruled 20 25 27—31 51 59 60 131 132 199 209 217 222 224 420 494
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