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| Kodaira K. — Complex manifolds and deformation of complex structures |
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| Предметный указатель |
 -closed form 88
-closed vector (0, q)-form 266
-cohomology group 140
-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  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,  -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, -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  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  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  function 109
Local  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 30
Non-singular prime divisor 167
Norm 148
Number of moduli 215 227 228 305 314
Obstruction 209 255
Obstruction,  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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