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| Авторизация |
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| Fischer G. — Complex Analytic Geometry |
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| Предметный указатель |
Active 144
Analytic algebra 14
Analytic intersection 24
Analytic inverse image 3 53
Analytic set 10
Analytic spectrum 59 70 116 123
Analytic tensor product 25
Analytically rare 37
Annihilator 37
Biholomorphic 10
Biholomorphic, locally 19
Blowing up of a complex subspace 162
Cartan — Serre, Finiteness theorem of 64
Cartan's Coherence theorem 8
Cartesian square 22
Cartier's theorem 50
Change of base 53
Chow's theorem 50 171
Clements' theorem 124
Closure 41
Coherence 3
Cokernel of a double arrow 66
Complex manifold 10
Complex space 9
Complex space, germ of a 16
Complex space, reduced 12
Complex spaces, direct product of 22
Complex spaces, fibre product of 21
Complex spaces, gluing data of 20
Cone 44
Cone, projective 49
Constructible 43
Corank of a coherent module 94
Corank, differential 97
Corank, geometric 135
Degeneracy set 136
Degeneracy set, analyticity of 131
Denominator, sheaf of analyticities 174
Denominator, universal 111
Derivation 77 85
Diagonal 27
Diagonal map 27
Differential corank 97
Differential form 84
Differential rank 97
Differential regularity criterion 96 100
DIMENSION 131
Dimension formula 142ff
Dimension, embedding 79
Direct image 1
Direct product 22
Double arrow, cokernel of 66
Double arrow, kernel of a 30
Duality theorem 51
Embedding 19
Embedding dimension 79
Equivalence relation 66
Equivalence relation, analytic 68
Equivalence relation, proper 74
Factorization lemma 138
Fibre 23
Fibre coproduct 68
Fibre product 21
Fibre space, linear 50
Finite algebra 60
Finite coherence theorem 58
Finite map 56 57 131
Finiteness theorem of Cartan — Serre 64
Flat 108 146ff
Flatification 156
Gap sheaf 37
Generation of a holomorphic map 18
Geometric corank 135
Geometric rank 135
Germ of a complex space 16
Gluing data 20
Graph theorem 126
graphs 178ff
Hilbert's Nullstellensatz 11 12 58
Holomorphic function 11
Holomorphic function, weakly 110
Holomorphic graph 180
Holomorphic map 10
Holomorphic map, restriction of a 13
Holomorphically complete 32
Holomorphically complete convex 32
Holomorphically complete convex, weakly 32
Holomorphically complete regular 32
Holomorphically complete separable 32
Holomorphically complete spreadable 32
Hopf bundle 165
Hurwitz's theorem 184
Hypersurface 42 162
Identity theorem for complex subspaces 41
Identity theorem for meromorphic functions 176
Image of a holomorphic map 65 37
Image sheaf 1 63
Immersion 19 100
Indeterminacy, point of 177
Integrity lemma 118
Inverse image of a complex space 23
Inverse image, analytic 3
Inverse image, topological 1
Invertible sheaf 42
Jacobian map 78 81 83
| Kernel of a double arrow 30
Kodaira — Spencer Sequence 106
Krull dimension 131
Levi's removable singularity theorem 185
Linear coefficient ideal 179
Linear fibre space 50
Linear fibre space, holomorphic sections in a 53
Linear fibre space, linear form on a 51
Local model 9
Local ringed space 1 66
Locally trivial 106
Maximal complex space 111
Maximalization 123
Maximalizations, lifting to the 125
Maximum Modulus Principle 132
Meromorphic function 173
Meromorphic graph 180
Mersion 99
Modification 142 162
Modification, proper 169
Monoidal transformation 162
Multiple point 10
Nilradical 11
Non-flat locus 155
Non-maximal locus 122
Non-normal locus 112
Normal complex space 111
Normal ring 112
Normal space of a complex subspace 163
Normal space of a holomorphic map 103
Normalization 112
Normalizations, lifting to the 121
Oka's coherence theorem 8
Open holomorphic maps 133 156
Open mapping principle 132
Ordinary point 96
Petrification 72
Pfaffian form 84 105
Pole variety 174
Primary decomposition 40
Principal sheaf 42
privileged 34
Projective algebraic 183
Proper 56
Proper coherence theorem 64 69
Purity of branch theorem 170
Rank, differential 97
Rank, geometric 135
Reduction 12
Regularity criterion, differential 96
Regularity criterion, relative 100
Relatively algebraic 171
Remmert — Stein — Thullen theorem 185
Remmert's mapping theorem 64
Resolution of singularities 168
Retraction 102
Riemann's removable singularity theorems 108 120
Ritt's lemma 41 117
Rossi's theorem 91
Segre embedding 172
Semicontinuity of dimension 131
Semicontinuity of fibre dimension 134
Semiproper mapping theorem 65
Sheaf 1
Sheaf of annihilators 37
Sheaf of denominators 174
Sheaf of finite presentation 3
Sheaf of finite type 3
Sheaf of ideals, full 9
Sheaf of relations 3
Sheaf of transporters 37
Sheaf, coherent 3
Sheaf, gap 37
Sheaf, invertible 42
Sheaf, linear space associated to a 51
Sheaf, locally free 3
Sheaf, principal 42
Sheaf, projective variety associated to a 55
Sheaf, support of a 4
Singular locus of a coherent module 95
Singular locus of a complex space 9 96
Singular locus of a holomorphic map 97
Spreading 134
Stein factorization 71
Stein space 32 127
Submersion 100
subspace 10
Syzygy 163
Tangent space 77 81
Tangent space of a holomorphic map 83
Tangent vector 77
Theorem A 33
Theorem B 33
Transporter ideal 37
Trivial 106
Universal denominator 111
Vector bundle 53
Vector field 85
Vector field, restriction of a 90
Weakly holomorphic 110
Weierstrass — Siegel — Thimm, theorem of 188
Weierstrass' preparation theorem 58
Zariski's main theorem 187
Zariski-semicontinuous 135
Zero-section 50
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