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| Griffiths P., Harris J. — Principles of algebraic geometry |
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| Предметный указатель |
Heimitian metric 27 71
Hermitian vector bundle 72
Hirzebruch — Riemann — Roch formula 437
Hodge conjecture 163
Hodge decomposition on cohomology 116
Hodge decomposition on forms 84
Hodge diamond 117
Hodge filtration 444
Hodge identities 111
Hodge metric 191
Hodge theorem 84 116
Hodge — Riemann bilinear relations 123
Holomorphic Euler characteristic 246 436
Holomorphic Lefschetz fixed point formula 430
Homogeneous algebraic variety 326
Homogeneous coordinates 15
Homotopy formula for Bochner — Martinelli 384
Hopf fibration 465
Hopf index theorem 421
Hopf surface 16
Hypercohomoiogy 446
Hyperelliptic curve 247 253 362
Hyperelliptic involution 253
Hyperelliptic surface 585 590
Hyperelliptic Weierstrass point 274
Hyperflex 547
Hyperplane 15
Hyperplane bundle 145 150 164
Hypersurface, algebraic 107
Hypersurface, analytic, Identity theorem 7
Implicit function theorem 19
Incidence correspondence 182
Incidence divisors 781
INDEX 125
Index theorem 126 471 472
Infinitely near point 185 482
Inhomogeneous form 166
Intermediate Jaeobian 331 802
Intersection of currents 392
Intersection of currents, cycle 53
Intersection of currents, index 49 51
Intersection of currents, multiplicity 62 64 65
Intersection of currents, number 49 51 63 392 470 663
Intersection of currents, pairing 52
intersection of three in  259
intersection of three in  592
intersection of three in , linear spaces on 735—741
intersection of three in , linear systems of 530 741
intersection of three in , lines on 199
Invariant polynomial 402
Inverse function theorem 18
Irrational ruled surface 553
Irreducible 12 21
Irregular linear system 245
Irregularity 494
Isogerty 329
Iwasawa Manifold 444
Jacobi inversion theorem 235 336 340
Jacobi relation 671
Jacobian of map 17
Jacobian variety 228 235 306 327 333 496
Jacobian variety, intermediate 331 802
K-3 surface 583 590 596 770 775 see "Quartic
Kahler manifold 109
Kahler metric 72 107
Kodaiia number 573
Kodaira classification of surfaces 590
Kodaira embedding theorem 181—191 207 209 214
Kodaira identity 100
Kodaira — Nakano vanishing theorem 128 154
Kodaira — Serre duality 1 02 153
Koszu] complex 688
Kummer surface 763
Kunneth formula 58 104
Lagrange interpolation 671
Laplacian 82
Lefschetz decomposition 122
Lefschetz fixed point formula 421
Lefschetz hard Lefschetz theorem 122
Lefschetz hoiomorphic Lefschetz number,. 424
Lefschetz hyperplane theorem 156
Lefschetz number 421
Lefschetz pencil 509
Lefschetz theorem on (l,l)-classes 163
Lefschetz theorem on theta-functions 317
Lefsltcetz holomotphie fixed point formula 430
Lelong number 391
Leray spectral sequence 463
Leray theorem 40
Levi extension theorem 396
Lichnerowicz lemma 711
Lie group, complex 325
Line bundle 66 132
Line bundle on projective space 145 165
Line bundle, associated to divisor 134
Line bundle, Chern classes of 139 144
Line bundle, degree of 144 214
Line bundle, positive/negative 148
Line bundle, tautological 605
Line bundle, very ample 192
Line complex, linear 759
Line complex, linear, quadric 762
Linear equivalence of divisors 134 161
Linear subspace 15
Linear system 137 176
Linear system of conics 484 497 741
Linear system of plane cubies 480 551
Linear system of quadrics 744
Linear system, dimension of 137
Linear system, irregular 245
Linear system, proper transform of 476
Linear system, special 245
Local defining function 130 132
Local duality theorem 659 693
Local ring 10 678
Log complex 449
Logarithmic transformation 566—568
Long Exact Sequence 40
Luroth's theorem 541
Map of sheaves 36
Maximal ideal 10
Maximum principie 7
Meromorphic function 36 168
Meromorphic section 13
Minimal degree 173
Minimal surfaces 552
Mittag — Leffler problem 34
Mobius configuration 760
Module 679
Monodromy group 467
Morse theory 157
Multiple fibers 564
Multiplicity 20 22
Multipliers 308
Nakayama lemma 680
Natural orientation 18
Negative line bundle 148
Neron-Severi group 454 461
Net 137
Node 215
Noether "AF + BG" theorem 703
Noether formula 438 472 601
Noether lemma 513
Noether theorem 253
Noetherian ring 679
Nondegenerate curve 253
Nondegenerate variety 173
Normal bundle 71 145
Normal crossings 449
Normal form for singularities of surface 618
| Normal form of curve 266
Normal variety 177
Normal Weierstrass point 274
Normalized basis 231
Normalized period matrix 305
Nullstellensatz 11 660 669
O(D) 138 139
Oka's lemma 695
Order 130
Ordinary double point of curve 215 278
Ordinary double point of surface 636
Ordinary m-fold point of surface 636
Ordinary singularities of surface 618
Ordinary triple point of curve 508
Ordinary triple point of surface 617
Orientation, natural 18
Osculating k-plane 264
Partition of unity 42
Pascal's theorem 673
Pencil 137
Pencil of tines 758
Period matrix 228 231 304
periods 226 228
Perturbation 657
Pfaffian 328
Picard group 133 161 235 313
Picard number 457 593 594
Picard variety 313 461
Pieri's formula 203
Pinch point 617
Plane of pencil of lines 758
Plucker coordinates 193 354
Plucker embedding/map 209 756
Plucker formulas 269 270 280
Plucker relations 211
Pluricanonical ring 573
Plurigenera 494 558 572 580
Plurisubharmonic function 387
Poincare duality 53
Poincare Formula 350
Poincare lemmas 25 38 385 450
Poincare line bundle 328
Poincare residue map 147 221 500
Poincare — Lelong equation 388
Poisson formula 379
Polarization 306
Polycylinder, punctured 445
Porteous' formula 415
Positive (1,1)-form 29
Positive current 386
Positive curvature operator 78
Positive divisor 148 307
Positive line bundle 148 307
Primitive cohomology 122
Primitive cycles 159
Principal part 34
Principal polarization 306
Projective bundle 515
Projective module 681
Projective resolution 683
Projective space 15
Projective space, automorphisms of 64
Projective space, canonical bundle of 146
Projective space, Cliern classes of 409 413 433
Projective space, cohomology of 60
Projective space, Hodge numbers of 118
Projective space, line bundles on 145
Projective space, subvarieties of 167
Propagation principle 696
Proper mapping theorem 34 395
Proper mapping theorem for finite maps 668
Proper transform 474 495
Proper transform of linear system 476
Pseudo-metric 268
Pullback divisor 132
Punctured polycylinder 445
Quadratic transformation 497
Quadric line complex 762
Quadric surface 478 484 744
Quadric surface, lines on 298 478
Quadrics 495 529 592 734
Quadrics, intersection of two in 550 630
Quadrics, intersection of two in 762
Quadrisecant 295 299
Quartic plane curve 256 281 546—549 770
Quartic plane curve with double point 770
Quartic plane curve, bitangent tines to 282 549
Quartic surface 591 764
Quartic surface in 550
Quartic surface with ordinary singularities 630—632
Quartic surface with two double lines 531 630
Quartic surface, Fermat 541
Quartic surface, with 16 double points 763
Quasi-isomorphism 446
Quintic Fermat surface 572
Quintic plane curve 535
Quotient bundle 68
Quotient sheaf 37
Ramification divisor 668
Ramification index of branched curve 217
Ramification index of curve in projective space 264
Rank of bundle 66
Rank of quadric 734
Rational functions 167
Rational map 490493
Rational normal curve 179 270 523 530 631
Rational normal scroll 525 532 631
Rational ruled surface 514
Rational surface 513 536
Real genus 500
Reciprocity laws 230 241 242
Regular sequence 659 688
Regularity lemma 94
Reiss relation 675 698
Rellich lemma 88 93
Residue of complete intersection 714
Residue of complete intersection of differential 454
Residue of complete intersection of singular form 369
Residue of complete intersection, n-variables 649
Residue of complete intersection, Poincare 1 47 221 500
Residue of complete intersection, theorem 222 656
Residue of complete intersection, theorem for vector bundles 731
Resolution of singularities 621
Resultant 9 12—14
Ricci curvature 97
Riemann bilinear relations 123 231 232
Riemann conditions 303 304 306 327
Riemann count 255—256
Riemann extension theorem 9
Riemann metric 28
Riemann relation 438 601
Riemann surface 15 215
Riemann Theorem 338
Riemann theta-divisor 321
Riemann theta-function 320
Riemann — Hurwitz formula 216 219
Riemann — Kempf singularity theorem 348
Riemann — Roch formula 245 248 437 472 600
Ruled surface 558 573 575 580
Ruled surface, irrational 553
Ruled surface, rational 514
S Metric connection 73
Scheme 697
Schubert calculus 197
Schubert cycles 196 353
Second fundamental form 78
Section 68
Section, meromorphic 1 35
Segre map 192
Sextic Enriques surface 632
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