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| Kobayashi S. — Differential geometry of complex vector bundles |
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| Предметный указатель |
ample 95 96
Ample, very 95
Analytic sheaf 154
Analytic sheaf, coherent 155
Appell — Humbert, theorem of 127
Approximate Einstein — Hermitian structure 118 183 234
Bianchi identity 3
Bogomolov’s inequality 114 120
Bott’s vanishing theorem 75
Chen — Ogiue’s inequality 116—117
Chern class, (semi-) negative 68
Chern class, (semi-) positive 68
Chern class, character 33
Chern class, class, total 30
Coherent analytic sheaf 155
Connection 1 4
Connection of degree (1, 0) 10
Connection, connection form 1
Connection, h-connection 11
Connection, Hermitian connection 12
Covariant derivative 2
Curvature 3
Curvature, curvature form 3
Curvature, mean 26 51
Curvature, Ricci 26
Curvature, scalar 26
Curvature, semi-negative 90
Curvature, semi-positive 91
d"-cohomology 66
Degree of vector bundle, sheaf 54 133 168
Degree/rank ratio of vector bundle 134 168
Depth 145 (see also “Homological codimension”)
Determinant bundle 18 162
Dolbeault, cohomology 66
Dolbeault, isomorphism 66
Donaldson’s Lagrangian 197
Dual of a module 150
Dual of a sheaf 159
Einstein, condition 59 99 118 226
Einstein— Hermitian vector bundle 59 99 138 176 262
Factor of automorphy 123
Factor of automorphy, theta 127
Finite type, module of 140
Flat, connection 5
Flat, Hermitian structure 14
Flat, structure 4 6
Flat, vector bundle 5 42
Fundamental 2-form 26
Gauge group 197
Gauss — Codazzi equations for subbundle 23
Gigante’s vanishing theorem 69
Girbau’s vanishing theorem 69
Green’s operator 67 252
h-connection 11
Harder — Narasimhan filtration 137 174
Harmonic form 66 252
Hermitian, connection 12
Hermitian, manifold 25
Hermitian, metric 10 25
Hermitian, structure 10 196 238
Hermitian, vector bundle 10
Hodge theorem 66
Holder space 210
Holomorphic structure in vector bundle 9 239
Holonomy group 2
Homogeneous Einstein — Hermitian vector bundle 120 183—184
Homological codimension (depth) 145
Homological dimension 144
Inequality of Bogomolov 114 120
Inequality of Chen — Ogiue 116—117
Inequality of Lubke 114 120
Jordan — Holder theorem 175
Kahler form 26—27
Kahler manifold 27
Kahler metric 27
Kodaira’s vanishing theorem 68
Kuranishi map 254 264
Le Potier’s vanishing theorem 80
Line bundle, ample 95
Line bundle, negative 68
Line bundle, positive 68 74
Line bundle, semi-negative 68
Line bundle, semi-positive 68 74
Line bundle, very ample 95
Locally finitely generated sheaf 154
Lubke’s inequality 114 120
m-sequence 145
Maximal semistable subbundle 136
Maximum principle for parabolic equaion 205
Mean curvature 26 51
Moduli space of Einstein — Hermitian structures 243 262 274
Moduli space of holomorphic structures 239 253
Moduli space of simple holomorphic structures 261 283
Momentum map 269
Nakano’s formula 66
Nakano’s inequality 69
Nakano’s vanishing theorem 68
Nakayama’s Lemma 140
Negative Chern class 68
Negative line bundle 68
Negative vector bundle 83 84 92
Normal frame field 13
| Normal sheaf 160
Null correlation bundle 122
Oka’s lemma 155
Orthonormal frame field 11
parallel 2
Positive Chern class 68
Positive line bundle 68 74
Positive vector bundle 83 84 92
Projective module 141
Protectively flat bundle 7 42 114 123
Protectively flat bundle, connection 7
Pseudoconvex 74
Pseudoconvex, strongly 88
Quotient bundle 20
Rank of module 149
Reduced phase space 270
Reduction theorem of Marsden — Weinstein 271
Reflexive module 151
Reflexive sheaf 159
Ricci curvature 26
Ricci form 19
Riemann — Roch formula 43
Scalar curvature 26
Second fundamental form 21 26 226
Semi-negative Chern class 68
Semi-negative curvature 90
Semi-negative line bundle 68
Semi-negative vector bundle 83 88
Semi-positive Chern class 68
Semi-positive curvature 91
Semi-positive line bundle 68 74
Semi-positive vector bundle 83
Serre duality 67
Sheaf homomorphism 101
Sheaf, coherent analytic 155
Sheaf, semi-stable 168 184 189 191
Sheaf, stable 168 184 189 191
Simple holomorphic structure 261 283
Simple vector bundle 173
Singularity set of a sheaf 155
Slice 254 263
Sobolev embedding 210
Sobolev inequality 210
Sobolev space 209
Stable 134 168 191
Stable, Gieseker semi-stable 189
Stable, Gieseker stable 189
Stable, H- 168 189
Stable, H-semi- 168 189
Stable, semi- 134 168 226
Stable, T- 134 184
Stable, T-semi- 134 184
Strongly, plurisubharmonic 85
Strongly, q-pseudoconvex 88
Subbundle 20
Symplectic form 47 269
Symplectic group 44
Symplectic structure 47 269 283
Symplectic transformation 269
Symplectic vector bundle 45
Syzygy, module 149
Syzygy, sheaf 158
Tautological line bundle 31
Torsion element 150
Torsion module 151
Torsion submodule 150
Torsion subsheaf 159
Torsion-free, module 150
Torsion-free, sheaf 159
Unitary frame field 11
Vanishing theorem of Bott 75
Vanishing theorem of Gigante 69
Vanishing theorem of Girbau 69
Vanishing theorem of Kawamata 73
Vanishing theorem of Kodaira 68
Vanishing theorem of Le Potier 80
Vanishing theorem of Nakano 68 74
Vanishing theorem of Ramanujam 73
Vanishing theorem of Takegoshi — Ohsawa 74
Vanishing theorem of Umemura 73
Vanishing theorem of Vesentini 68
Vanishing theorem of Viehweg 73
Vector bundle, ample 96
Vector bundle, associated 15
Vector bundle, defined by a representation 6 14
Vector bundle, flat 5
Vector bundle, Gieseker semistable 189
Vector bundle, Gieseker stable 189
Vector bundle, negative 83 84 92
Vector bundle, positive 83 84 92
Vector bundle, projectively flat 7 42 123 138
Vector bundle, semi-negative 83 88
Vector bundle, semi-positive 83
Vector bundle, semi-stable 134 168 191 226
Vector bundle, simple 173
Vector bundle, stable 134 168 191
Vector bundle, T-semi-stable 134 184
Vector bundle, T-stable 134 184
Very ample 95
Vesentini's vanishing theorem 68
Weak Einstein condition 99
Weakly 1-complete 74
Weighted flag 134 184
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