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| Catanese F. (Ed) — Global Aspects of Complex Geometry |
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| Предметный указатель |
 see Deformation space of a surjective morphism
 , locus of chains of rational curves through a point 389
 see Moduli space of vector bundles on a curve
 (AT) see Space of rational curves on a variety
 -adic cohomology 60 65
(a,b,c)-surfaces 45
(k, l)-stable sheaf 394
1-form 133
a.q.c.d.-equivalence 49
Abel Jacobi map 455
Abundance conjecture 321 324
Adapted complex structure 257
Additive Chow groups with higher modulus 69
Additive higher Chow groups 67 68
Adjoint representation 230
Affine symmetric space 235
Algebraic approximation 329
Algebraic cycle 451
Algebraic group 229
Almost Fano 340 346 348 350
Almost holomorphic map 365
Ample Cartier structure 246
Ample cone 313
Analytic family of cycles 245
Analytic type 178
Anti-Zariski pair 198
Anticanonical map 340 342
Anticanonical model 310
Arakelov inequality 418 420
Arakelov, Sergei J. 405
Artin — Schreier 75
Artin's braid group 37
Asymptotically optimal condition 173
Asymptotically proper condition 173
Automorphic representation 281
Automorphic representation, cuspidal 282
Ax-Katz 63 64
Bands and strings 104 105 107 110
Base cycle 248
Base points 341 343 344
BDPP, Theorem of Boucksom, Deailly, Peternell, Paun 359 361
Beauville surfaces 31
Bend-and-break 368 370
Bloch Beilinson filtration 466
Bloch's decomposition of the diagonal 62 63 65
Bogomolov, Fedor A. 362 364 366
Borel subalgebra 232
Borel's fixed point theorem 238
Borel. Armand 398
Bore] subgroup 232
Boucksom. Sebastien 359 see
Bunches of chains 83 102 104 107 117
Calabi — Yau threefold 285 303
Calabi — Yau threefold, rigid 281 285 291
Calabi — Yau variety 271 284 302
Campaiia. Frederic 364
Cartan decomposition 211—213
Cartan involution 221
Cartan — Fubini type theorem 387
Cartan — Fubini type theorem for varieties covered by lines 360
Cartan, Elie 360 379 387.
Cauchy characteristic of a distribution 386
Cauchy subvariety 387
cDV singularity 338 344 353
Characterization of  386
Chazy's equation 460
Chevalley's Theorem 229
Chow scheme 245
Chow — Kuenneth decomposition 461
Co-adjoint orbit 220—222
Coadjoint orbit 240
Completely reducible 231
Complex multiplication 271 283 289 291
Complex radial index 137
Cone like singularity 133
Congruences 60 66 67
Connecting family 322 321
Contact manifold 388 390
Contact manifold, uniqueness of contact structure 359 388
Crystalline cohomology 60
Cusp 173
Cusp form 277
Cycle space 243
de Jong's alteration 65
de Rham complex 73
de Rham — Witt complex 70
def-equivalence 43
Deformation of a surjective morphism 360 see
Deformation pattern 189
Deformation rigidity of certain varieties 388
Deformation rigidity of Hermitian symmetric spaces 359
Deformation space of a surjective morphism 398—404
Deformation space of a surjective morphism, description of 399 401
Deformation space of a surjective morphism, dimension of 399
Deformation space of a surjective morphism, relative over the rationally connected quotient 400
Deformation space of a surjective morphism, when target is not uniruled 398—399 401 404
Degree of a Fano threefold 310 341
Dehn twists 39
Deligne cohomology 455
Demailly, Jean-Pierre 359 see
Determinant line bundle 481 482 489
Diffeomorphism 133
Differential system 386
Divisibility 60 62
Divisorial contraction 342
Doligne's integrality theorem 61 65
du Val double planes 14
Elementary transform 394
Emerton 76
Emerton — Kisin correspondence 76
Equianalytio family 177
Equisingular family 171 178
Equisingularity stratum 179
Etale cohomology 72 274
Existence of curves 171
Extrasymmetric matrices 27
Fake projective planes 23
Faltings — Serre — Livne method 287 292
Faltings. Cord 405
Family of canonically polarized varieties 360 375 405—411 see Viehweg
Family of canonically polarized varieties of maximal variation 405
Family of canonically polarized varieties over  are isotrivial 409
Family of canonically polarized varieties, isotrivial 105
Family of canonically polarized varieties, theorem relating variation and log. Kodaira dimension of the base 106
Family of canonically polarized varieties, variation of 360
Family of curves 177
Family of rational curves 376 379. see also Space of rational curves on a variety
Family of rational curves, dominating 377
Family of rational curves, dominating of minimal degrees 376—379
Family of rational curves, dominating of minimal degrees, are generically unsplit 378
Family of rational curves, dominating of minimal degrees, has few singular members 376 379—383
Family of rational curves, generically unsplit 378
Family of rational curves, kth-spanning dimension of 389
Family of rational curves, maximal 177
Family of rational curves, unsplit 378
Fermat's last theorem 282
Fibrations of surfaces to curves 6
Flag manifold 238
Flenner, Hubert 362 403
Foliation 362 363 372 373 see
Foliation in positive characteristic 362
Foliation, special in the sense of Miyaoka 372
Fountain — Mazur conjecture 280 281 285
Fourier — Mukai transform 83 86 94 95 123—125
Frankel, Theodore 361
Frobenius 60 75
Frobenius morphism 274 276 285 297
Fubini — Study metric 212
Fubini, Guido 300 see
G-bundle 238
| Galois representation 271 276 278 303
Galois representation, coming from geometry 280
Galois representation, geometric 280
Gauss — Manin connection 299
Gelfand problem 83 87 102
General complete intersection curve 362 374 402
General elephant 346
Generalized hyperelliptic surfaces 18
Generic coverings 42
Generically nef 318 319
Geometric invariant theory 212
GHS Theorem, the base of the MRC fibration is not uniruled 359 365 367
Graber, Tom 359 365 see
Gradient vector field 138
Griffiths — Yukawa coupling 420
Groessencharacter 271 290 295
Grothendieck's generalized Hodge conjecture 64
Groupoid, fibered 472
GSV index of a 1-form 140
GSV index of a vector field 138
Hard Lefschetz theorem 314
Harder — Narasimhan filtration ample terms in 372 373
Harder — Narasimhan filtration ample terms in of the tangent bundle 363 372 374.
Harris, Joe 359 365 see
Hartshorne — Frankel conjecture 361
Hartshorne, Robin 361 367 370 372
Hartshorne, Robin, characterization of ampleness 370
Hecke curves 360 393—395
Hecke curves are free and smooth 395
Hecke curves are rational 395
Hecke curves form a dominating family 396
Hecke curves have minimal degree 395—397
Hecke eigenform 278
Hermite — Einstein connection 477
Hermitian semi-positive 313 334
Higgs bundle 420 424 463 483 484 486 490 492
Higgs bundle, stable 424
Higgs field, strictly maximal 420 435
Higher Chow group 452
Hilbert functor 178
Hilbert quotient 225
Hodge level 60
Hodge theory 451
Holomorphically convex 333
Holonomic  module 74
Homogeneous manifold 234
Homological index of a 1-form 141
Homological index of a vector field 141
Horing, Andreas 364
Hwang, Jun-Muk 361 376 385—388 395—397
Hyper — Kaehler structure 490 492
Hyperbolicity problems 375
Hyperelliptic 341 343 346 348
Incidence variety 245
Index of a collection of 1-forms 159
Index of a collection of vector fields 159
Index-one-cover 410
Integrable connection 73
Integrality theorem 61
Intermediate extension 77
Intersection cohomology 463
Isolated special point 162
Isotropy representation 214 215 221
Iwasawa — Borel subgroup 249
Iwasawa — Schubert variety 250
Iwasawa-envelope 258
Jacobi identity 230
Jahnke, Priska 359
K3 surface 285 288
K3 surface, singular 288 290 302
Kaehler cone 313 315 326
Kaehlerian form 211—213 220
Kaehlerian manifold 211 212 214 220
Keel, Sean 360 363 375 405 see
Killing form 240
Kisin 76
KMcK, rational curves on quasi-projective varieties 360 375
Kobayashi — Hitchin correspondence 473 494
Kodaira dimension of a quasi-projective variety see Logarithmic Kodaira dimension
Kodaira — Spencer map 396
Kollar, Janos 364 405
Kovacs, Sandor J. 405
Kummer construction 289 294
Kummer variety 317 327
L-function 275
Lang — Manin conjecture 60
Langlands' programme 281
Lazarsfeld, Robert 402
Lazarsfeld, Robert, Negativity theorem 402 403
Leaf of a foliation 363
Leaf of a foliation, algebraicity 362—364 366 367 374
Leaf of a foliation, rational connectivity 362—364 367 374
Lefschetz fibrations 40
Lefschetz trace formula 274 282 297
Length of a Fano manifold 376
Length of a uniruled manifold 388—393
Levi — Malcev factor 229
Lie's flag theorem 238
Link 133
Local Chern obstruction 163
Local cohomology 78
Local Euler obstruction of a 1-form 145
Local Euler obstruction of a function 144
Local system 74
Log minimal model of a surface 406 407
Logarithmic abundance 407
Logarithmic Kodaira dimension 360 363 375 405
Logarithmic Kodaira dimension of canonically polarized varieties, Shafarevich conjecture, Viehweg conjecture Lojasiewicz's inequality 219
Logarithmic Kodaira dimension of the base of a family see Family
Lyubeznik 78
Manifold with isolated singularities 133
Mapping class group 38
Matrix problem 83 86 98 101—103 119
Maximal Albanese dimension 9
Maximal compact subgroup 233
Maximal torus 231
Maximally ample subbundle 371 403
Maximally etale factorization 400
Maximally etale factorization, characterization 400
Maximally etale factorization, stability under deformations 400
Maximally etale factorization, universal property 400
Maximally rationally chain connected fibration 365 see
Maximally rationally chain connected fibration, universal property 305
McKernan, James 360 363 375 405 KMcK
McQuillan, Michael L. 362 364 366
Measurable orbit 252
Mehta — Ramanathan theorem 362
Mehta, Vikram B. 362 402 403 see
Mellin transform 279
Mirror Symmetry 299 305
Miyanishi, Masayoshi 375 405
Miyanishi, Masayoshi, conjecture on affine lines on quasi-projective varieties 375 405
Miyaoka, Yoichi 360 362 364 371 372 398
Miyaoka, Yoichi, criterion of uniruledness 300 398 402 403 409
Miyaoka, Yoichi, foliations in positive characteristic see Foliation
Modular curve 277
Modular form 271 277 283
Moduli for coupled vortex equations 492
Moduli of Higgs bundles 483
Moduli of holomorphic vector bundles 473
Moduli of principal bundles 476
Moduli space of vector bundles on a curve 360 385 388 393—398
Moduli space of vector bundles on a curve is sometimes Fano 394
Moduli space of vector bundles on a curve, automorphism group 397
Moduli space of vector bundles on a curve, rational curves of minimal degree 396
Moduli space of vector bundles on a curve, stability of the tangent bundle 397
Moduli space of vector bundles on a curve, tangent map for Hecke curves 396
Moduli space of vector bundles on a curve, Torelli-type theorem 397
Moduli space of vector bundles on a curve, variety of minimal rational tangents 396
Moduli space of vector bundles on a curve, variety of minimal rational tangents, secant defect 397
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