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Griffiths P., Harris J. — Principles of algebraic geometry
Griffiths P., Harris J. — Principles of algebraic geometry

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Название: Principles of algebraic geometry

Авторы: Griffiths P., Harris J.

Аннотация:

A comprehensive, self-contained treatment presenting general results of the theory. Establishes a geometric intuition and a working facility with specific geometric practices. Emphasizes applications through the study of interesting examples and the development of computational tools. Coverage ranges from analytic to geometric. Treats basic techniques and results of complex manifold theory, focusing on results applicable to projective varieties, and includes discussion of the theory of Riemann surfaces and algebraic curves, algebraic surfaces and the quadric line complex as well as special topics in complex manifolds.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1978

Количество страниц: 813

Добавлена в каталог: 01.07.2006

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$d_{c}$-operator      109
$S_{k,n}$      524
$S_{n}$      517
$\bar{\partial}$-Laplaeian      82
$\bar{\partial}$-operator      24 70
$\bar{\partial}$-Poincare lemma      5 25
$\delta$-function      367
$\mathbb{P}^{1}$, characterization of      222 see "Rational
$\mathbb{P}^{1}$, vector bundles on      145 516
$\mathbb{P}^{2}$, birational automorphisms of      496
$\mathbb{P}^{2}$, characterizations of      487 575 580
$\mathbb{P}^{n}$      see "Projective space"
(p,p), classes      163 416
(p,p), currents      385
(p,p), forms      23
(p,q)-forms      23
A-cycles      228
Abel's theorem      226 227 232 235
Abelian integrals      225
Abelian sums      226
Abelian surface      3 24 583 779
Abelian variety      301
Abelian variety, polarized      359
Acyclic covering      40 45
Addition theorem      240
Adjunction,formula      146 147 157 220 471
AF + BG theorem      703
Affine algebraic variety      453
Albanese map/variety      331 552
Algebraic curve      215
Algebraic de Rham theorem      45 3
Algebraic equivalence of divisors      461
Algebraic variety      128 166
Algebraic variety, affine      453
Algebraic variety, homogeneous      326
Algebraic variety, nondegenerate      173
Algebraic variety, normal      177
Antiholomorphic      17
Arithmetic genus      494
Associated curve      263
Associated line bundle      134
Automorphisms of Abelian varieties      326
Automorphisms of hypersurface      178
Automorphisms of projective space      64
Automorphisms of Riemann surface      275 276
B-cycles      228
Base locus      137 176
Bertini's theorem      137 536
Bezout's theorem      172 670
Bianchi identity      406
Birational invarients      494
Birational maps      237 493 510
Bitangent line      278
Bitangential correspondence      294
Bitype      383
Blow-up of point      182 373 473 510 558
Blow-up of submanifold      603 749
Bochner — Martinelli kernel      383 425 655
Bochner — Martmelli formula      372 384 426 433 655 666
Bott residue formula      427 437
Branch locus      217 668
Branch point      217
Brill — Noetiler problem      260
Canonical basis      227
Canonical bundle      146
Canonical bundle of blow-up      187 608
Canonical bundle of divisor      147
Canonical bundle of projective space      146
Canonical curve      247 535
Canonical map      247
Cartan structure equations      75
Castelnuovo curves      527
Castelnuovo lemma      531
Castelnuovo — de Franchis theorem      554
Castelnuovo — Enriijues theorem      536
Castelnuovo — Enriques criterion      476 505
Cauchy integral formula      2
Cauchy kernel      369 663
Cauchy — Rjemann equations      2
Cayley — Bacharach      671
Cayley — Bacharach for vector bundles      731
Cayley — Bacharach, property      671
Cayley — Brill formula      287
Cech cohomology      35 39
Chern classes      407
Chern classes of blow-up      608
Chern classes of line bundle      139 144
Chern classes of projective space      409 413 433
Chern — Gauss — Bonnct theorem      410 413 416
Chordal variety      173
Chow's theorem      167
Classification theorem for surfaces      590
Clifford's theorem      251
Coboundary      38
Cochain      38
Cocycle      39
Coframe      28
Coherent sheaves      181 696
Cohomology of blow-up      473 605 751
Cohomology of compiex      439
Cohomology of currents      382
Cohomology of Grassmannians      205
Cohomology of projective bundles      606
Cohomology of projective space      60
Cohomology, analytic      162
Cohomology, Cech      35 39
Cohomology, de Rham      2 3
Cohomology, Dolbeault      25 80 100 150
Cohomology, primitive      122
Cohomology, simplicial      42
Cohomology, singular      43
Coincident point      283
Common point      284
Complete linear system      137
Complex manifold      14 20
Complexes      438 682
Complexes of sheaves      445
Complexes, double      442 685
Complexes, homology and cohomology of      682
Cone      172 734
Conics      529 55.1 630 673
Conics, five      749
Conics, linear systems of      484 497 741
Connection      72 400
Conormal bundle      71 145
Continuity principle      657
Coordinates, Euclidean      15
Coordinates, euclidean, holomorpbic      14
Coordinates, euclidean, homogenous      15
Coordinates, euclidean, Plucker      193
Correspondence      282
Correspondence, associated to pencil      283
Correspondence, bitangentiai      294
Correspondence, tangential      283
Correspondence, trisecant      291
Cousin problem      47
Covering, branched      9 217 255
Covering, branched, unbrancheil      192 542
Cremona transformation      496
Cubic plane curve      222 280 599 673 704
Cubic plane curve, linear system of      480 551 see "Elliptic
Cubic surfaces      480 545
Cubic surfaces in $\mathbb{P}^{4}$      531 629
Cubic surfaces with doubie ine      531 629
Cubic surfaces with ordinary double points      640—646
Cubic surfaces, lines, on      485 522 546
Currents      368
Currents, positive      386
Curvature      75 140 401
Curve of correspondence      282
Curves of genus 0      222 see
Curves of genus 1      222 238 286 see "Elliptic
Curves of genus 10      593
Curves of genus 2      298 359 770 782
Curves of genus 3      256 281 546—549 770 see
Curves of genus 4      258 298 359
Curves of genus 5      259
Curves of genus 6      298 349 359 see
Curves of genus 8      299 359
Cusp of curve      277
Cuspidal point of surface      617
de Rham, cohomology      23
de Rham, isomorphism      45
de Rham, theorem      44 447
de Rham, theorem, algebraic      453
Decomposable holomorphic vector bundle      516
Deficiency of linear system      628
Degeneracy set      411
Degree, of line bundle      144 214
Degree, of line bundle of 0-cycle      667
Degree, of line bundle of map      217 666
Degree, of line bundle of variety      171 172
Desingularization of algebraic curve      498 506
Desingularization, theorem of Hironaka      621
Differentials of first kind      124 230 241 454
Differentials of second kind      231 241 454 460
Differentials of third kind      231
Dimension of linear system      137
Dimension of variety      22 173
Direct image stieaf      463
Directrix of rational normal scroll      525
Dirichlet norm      93
Distributions      90 366
Divisor      130
Divisor of function      131
Divisor of section      135
Divisor with normal crossings      449
Divisor, algebraic equivalence of      461
Divisor, effective      130 238
Divisor, exceptional      182 603
Divisor, exceptional (of first kind)      478
Divisor, line bundle associated to      134
Divisor, linear equivalence of      134 161
Divisor, very ample      192
Divisors, elementary      306
Doibeauit cohomology      25 80 100 150
Doibeauit complex      448
Doibeauit theorem      45 100
Double curve of surface      612
Double points of curve, cusp      277
Double points of curve, ordinary      215 277
Double points of curve, tacnode      293 507
Double points of surface, ordinary      636
Double points of surface, pinch or cuspidal point      617
Double points of surface, transverse      616
Dual bundle      66
Dual cell decomposition      53
Dual curve      264
Dual Kummer surface      763
Dual projective space      15
Dual Schubert cycle      200
Dual, Abelian variety      314
Effective 0-cycle      667
Effective divisor      130 238
Elementary divisors      306
Elementary invariant polynomials      402
Elliptic curve      222 225 238 286 564 575 586 see "Curves
Elliptic surface      564 573 574
Elliptic surface with rational base      577 see "Hyperelliptic and
Enriques classification of surfaces      590
Enriques surface      544 583 594 599 632 749
Enriques theorem      580
Enriques-Petri theorem      535
Equivalence of divisors, algebraic      461
Equivalence of divisors, linear      134 161
Euclidean co-ordinates      15
Euclidean metric      30
Euler      673
Euler characteristic of branched cover      218 508 548
Euler characteristic of curve      218 508
Euler characteristic of surface in space      601 625
Euler characteristic of surface with pencil      509—510
Euler characteristic, holomorptiic      246 436
Euler characteristic, topological, of blow-up      474
Euler sequence      409
Exact sequence of sheaves      37
Exact sequence, long      40
Exceptional divisor      182 603
Exceptional divisor of first kind      478
Exponential map      325
Exponential sheaf sequence      37
Ext of modules      684
Ext of sheaves      700
Extensions of Modules      722
Fermat quartic surface      541
Fermat quintic surface      572
Fiber bundle, holomorphic      514
Fiber of coherent sheaf      700
Fiber of vector bundle      66
Fine sheaf      42
Finite cycles      123
Five conics      749
Fixed component      137
Fixed point formulas      421 430
Flag      60 194
Flat vector bundle      465
Flex      277
Flex, hyper-      547
Focus of pencil of lines      758
Form,holomorphic      24 110 148
Form,holomorphic, type (p,q)      23
Frame      68
Frohlicher relations      444
Frohlicher spectral sequence      444
Fubini — Study metric      31 109 373
Functions, analytic      2 6
Functions, holomorphie      2 6
Functions, meromorphic      36 168
Fundamental class      61 140 144 356 386 475
Fundamental group      484
G(2,4)      197 290 297 630 746 756
G(2,6)      611 778
G(3,6)      772
G.A.G.A. principle      171
Gap values      273
Garding's inequality      93 97 381
Gauss map      264 360 496 735
Gauss — Bonnet formula      144 216 410 413 416
Gaussian curvature      77
General type      573
GENERIC      20
Genus      216
Genus formula      219
Genus, arithmetic      494
Genus, geometric      494
Genus, real      500
Genus, virtual      471
Geometric genus      494
Gjambelli's formula      205
Global duality theorem      707 708
Godeaux surface      572
Graph of rational map      492
Grassmannian      193
Green's function      378
Green's operator      84 90 96 149
G{2,5)      550
Hard Lefschetz theorem      122
Harmonic forms      82 83 152 376
Harmonic space      82 100 152
Hartog's theorem      7 49 165 494
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