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Fischer G. — Complex Analytic Geometry
Fischer G. — Complex Analytic Geometry

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Название: Complex Analytic Geometry

Автор: Fischer G.

Аннотация:

These Lecture Notes arose from courses held at the Universities of Regensburg, Frankfurt and Munich. The aim of the courses was to present a survey of the fundamental concepts and results of "complex analytic geometry" (i.e. the theory of functions of several complex variables) and to approach the current state of research in this field.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1976

Количество страниц: 201

Добавлена в каталог: 28.03.2010

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