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Kodaira K. — Complex manifolds and deformation of complex structures
Kodaira K. — Complex manifolds and deformation of complex structures

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Название: Complex manifolds and deformation of complex structures

Автор: Kodaira K.

Язык: en

Рубрика: Математика/Алгебра/Алгебраическая геометрия/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1986

Количество страниц: 465

Добавлена в каталог: 12.03.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$\bar{\partial}$-closed form      88
$\bar{\partial}$-closed vector (0, q)-form      266
$\bar{\partial}$-cohomology group      140
$\bar{\partial}$-cohomology group with coefficients in F      144
(0, q)-form with coefficients in F      142
(p, q)-form      86
(p, q)-form with coefficients in F      143
1-form      77
A priori estimate      275 396 430 432 436
Abelian variety      49
Admissible fibre coordinate      325
Affine algebraic manifold      40
Algebraic curve      40
Algebraic subset      40
Algebraic surface      40
Analytic continuation      9 10
Analytic function      10
Analytic hypersurface      19
Analytic subset      33
Arithmetic genus      220
Associate      15
Automorphism      43
Base space      97 184
Betti number      175
Biholomorphic      26
Biholomorphic map      26
Biholomorphically equivalent      32
Bott's theorem      244
Bracket      212
Bundle, canonical      164 178
Bundle, complex line      165 166 167
Bundle, dual      102
Bundle, tangent      96
Bundle, trivial      99
Canonical basis      358 361
Canonical bundle      164 178
Canonical bundle of $P^n$      178
Cauchy — Riemann equation      7
cell      169
Chern class      166
Chern class, first      180
Closed differential form      83
Coboundary      115
Cochain, q-cochain      115
Cocycle, g-cocycle      116
Codimension      234
Cohomology      109
Cohomology class      120
Cohomology group      115
Cohomology group with coefficients in a sheaf      116 120
Cohomology group with coefficients in F      144
Cohomology group, $\hat{\partial}$-cohomology group      140
Cohomology group, d-cohomology group      139
Compact      39
Compact complex manifold      39
complete      228
Complex analytic family      59
Complex analytic family of hypersurfaces      234
Complex analytic family, complete      228
Complex analytic family, effectively parametrized      215
Complex analytic family, induced by a holomorphic map      206
Complex analytic family, trivial      61
Complex dimension      29
Complex Laplace — Beltrami operator      154
Complex Lie group      48
Complex line      29
Complex line bundle      165 166 167
Complex manifold      28 29
Complex projective space      29
Complex structure      28 29 38
Complex torus      48
Complex torus, number of moduli of      238
Complex vector bundle      101
Component of a tangent vector      96
Component, contravariant      153
Component, covariant      153
Composite function      12
Constant of ellipticity      392 396 431
Constant of strong ellipticity      394 399 434
Contravariant component      153
Contravariant tensor field      107
Contravariant vector      106
Convergent power series      14
Coordinate multi-interval      127
Coordinate polydisk      32
Coordinate transformation      29
Coprime      15
Covariant component      153
Covariant tensor field      106
Covariant vector      106
Covering manifold      45
Covering transformation group      45
d-cohomology group      139
de Rham's theorem      134 139
Deformation      61
Deformation, infinitesimal      182 188 190 198
Determining set      2
Diagonal type      404 416 436
Diffeomorphism      38
Difference quotient operator      367
Differentiable family of compact complex manifolds      182 183 184 345
Differentiable family of complex vector bundles      324
Differentiable family of holomorphic vector bundles      346
Differentiable family of linear operators      325
Differentiable family of strongly elliptic partial differential operators      325
Differentiable family, locally trivial      193
Differentiable family, system of local coordinates of      185
Differentiable family, trivial      193
Differentiable manifold      37 38
Differentiable structure      37 38
Differential form      76
Differential form on complex manifolds      85
Differential form, closed      83
Differential form, exact      83
Differential form, harmonic      144 152 156 157
Differential operator      62
DIMENSION      33
Directed set      119
Discrete subgroup      48
Displacement      236
Displacement, infinitesimal      236
Distinguished polynomial      13
distribution      363 364
Distribution, vector-valued      368
Divisor      167
Dolbeault's lemma      88
Dolbeault's theorem      134 139 140
Dual bundle      102
Dual form      150
Dual space      102
Effective      215
Effectively parametrized      215
Eigenfunction      323
Eigenvalue      323
Elliptic curve      47
Elliptic curve, complex analytic family of      68
Elliptic modular function      69
Elliptic operator with constant coefficients      391
Elliptic partial differential equation      443
Elliptic partial differential operator      363 391 430
Elliptic partial differential operator, strongly      320
Elliptic surface      319
Elliptic type      392 395 431
Equicontinuous      276
Equivalent      99 109 192
Exact commutative diagram      133
Exact differential form      83
Exact sequence      123 126
Exterior differential      78
Fibre      97
Fibre coordinate      98
Fibre coordinate, admissible      325
Fine resolution      137
Fine sheaf      134
Fixed point      44
Form, $\bar{\partial}$-closed      101
Form, (0, q)-form with coefficients in F      142
Form, (p, q)-form      86
Form, (p, q)-form with coefficients in F      143
Form, 1-form      77
Form, dual      150
Form, harmonic      156
Form, harmonic with coefficients in F      160
Form, holomorphic p-form      88
Form, holomorphic p-form with coefficients in F      143
Form, r-form      77
Formal adjoint      152 439
Formally self-adjoint      156 321
Fourier series      373
Fourier series expansion      368
Friedrichs' inequality      330
Fundamental domain      47
Garding's inequality      399 433 435
Geometric genus      220
Germ      109
Green operator      275 315 323
Group of automorphisms      43
Harmonic differential form      144 152 156 157
Harmonic form      156
Harmonic form with coefficients in F      160
Harmonic function      9
Harmonic part      315
Harmonic vector (0, 1)-form      274
Hermitian metric      144
Hermitian metric on the fibres      158
Hoelder norm      274 303 403 436
Holomorphic      2
Holomorphic function      1 2 30
Holomorphic map      23 30
Holomorphic p-form      88
Holomorphic p-form with coefficients in F      143
Holomorphic vector bundle      101
Holomorphic vector field      67 69
Holomorphically equivalent      32 61
Homogeneous coordinate, of $\mathbb{P}^n$      29
Homomorphism, of sheaves      123
Hopf manifold      49 55
Hopf surface      69
Hopf surface, deformation of      208
Hypersurface      40
inclusion      124
Infinitesimal deformation      182 188 190
Infinitesimal deformation, along $\partial/\partial t$      198
Infinitesimal displacement      236
Inner product      102 147 425
Integrability condition      269
Integral domain      15
Intersection number      54
Irreducible      15
Irreducible equation      20
Irreducible factor      15
Irreducible factorization      15
Irregularity      220
Isomorphism, of sheaves      124
Jacobian      24
Jacobian matrix      24
Kahler form      174
Kahler manifold      174
Kahler metric      174
Kernel      123
Kronecker product      104
Kuranishi family      318
Laplacian      9
Lax — Milgram Theorem      440
Leibnitz' formula      367
Length, of a multi-index      363
Line at infinity      57
Linear partial differential operator      424
Local $C^{\infty}$ function      109
Local $C_{\infty}$ vector (0, q)-form      256
Local complex coordinate      28
Local coordinate      29
Local coordinate with centre q      32
Local equation      33
Local homeomorphism      110
Locally constant function      112
Locally finite open covering      32
Locally trivial      193
Majorant      277
Manifold, affine algebraic      40
Manifold, compact complex      39
Manifold, complex      28 29
Manifold, differentiable      37 38
Manifold, projective algebraic      40
Manifold, topological      37 38
Map, biholomorphic      26
Map, holomorphic      23 30
Meromorphic function      35
Minimal equation      22
Mixed tensor field      107
Modification      53
Monoidal transformation      319
Multiple      15
Multiplication operator      423
Noether's formula      220
Non-homogeneous coordinate, of $\mathbb{P}^n$      30
Non-singular prime divisor      167
Norm      148
Number of moduli      215 227 228 305 314
Obstruction      209 255
Obstruction, $\nu$th      255
Obstruction, first      214
Orbit      43
Order      321
Orientable      80
Orientation      80 86
PARAMETER      184
Parameter space      60 184
Parametrix      405
Partial derivative, of a distribution      366
Period matrix      48
Poincare's lemma      83
Point at infinity      57
Polydisk      2
Power series ring      14 15
Principal part      154 395 431
Principal symbol      392 395 431
Projection      97 112
Projective algebraic manifold      40
Projective space      174 216
Projective space, complex      29
Projective space, homogeneous coordinate of      29
Projective space, non-homogeneous coordinate of      30
Properly discontinuous      44
q-cochain      115
q-cocycle      115
Quadratic transformation      57
Quartic surface      307
Quotient sheaf      125
Quotient space      43
r-form      77
Rank      97
Rational function      42
Real vector bundle      101
Reducible      15
refinement      117
Region of convergence      7
Regular      17
Relatively prime      15 19 35
Rellich's theorem      427
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