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Kobayashi S. — Differential geometry of complex vector bundles
Kobayashi S. — Differential geometry of complex vector bundles

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Название: Differential geometry of complex vector bundles

Автор: Kobayashi S.

Язык: en

Рубрика: Математика/Алгебра/Алгебраическая геометрия/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1987

Количество страниц: 304

Добавлена в каталог: 12.03.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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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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