Complex analytic geometry:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
1976
|
| Series: | Lecture notes in mathematics
538 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | VII, 201 S. |
| ISBN: | 3540078576 0387078576 |
Staff View
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| 245 | 1 | 0 | |a Complex analytic geometry |c Gerd Fischer |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 1976 | |
| 300 | |a VII, 201 S. | ||
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| 650 | 4 | |a Fonctions de plusieurs variables complexes | |
| 650 | 4 | |a Analytic spaces | |
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Record in the Search Index
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|---|---|
| adam_text | Contents
page
Chapter 0. BASIC NOTIONS
0.1 Ringed spaces t
0.2 Direct an topological inverse images of sheaves 1
0.3 Morphisms of ringed spaces 2
0.4 Monomorphisms and epimorphisms 3
0.5 Finite type, finite presentation, coherence 3
0.6 4
0.7 S
0.8 Germs of homomorphisms 5
0.9 Extension of germs 6
0.10 Analytic inverse image of sheaves 6
0.11 Trivial extension of sheaves 8
0.12 Coherence Theorem of OKA 8
0.13 Coherence Theorem of CARTAN 8
0.14 Complex spaces, holomorphic maps, subspaces 9
0.15 Nilradical 11
0.16 Reduction 12
0.17 Restriction of a holomorphic map 13
0.18 Analytic local algebras 14
0.19 Holomorphic maps into I 14
0.20 Holomorphic maps of a reduced complex space 15
0.21 Germs of complex spaces 16
0.22 Generation of holomorphic maps 17
0.23 Immersions and embeddings 19
0.24 Gluing of complex spaces 20
0.25 Universal property of fibre products and products 21
0.26 Direct product of Cn and Tm 22
0.27 Inverse images of subspaces 23
0.28 Direct product of subspaces 24
0.29 Direct products (general case) 25
0.30 The diagonal 26
0.31 Universal property of the diagonal 29
0.32 Existence of fibre products 29
0.33 Kernel of a double arrow 30
0.34 Fibre products of reduced complex spaces 30
0.35 Immersion of holomorphic maps 31
0.36 Stein spaces 32
0.37 Theorems A and B 32
0.38 Characterization of Stein spaces 34
0.39 Privileged neighbourhoods 34
0.40 Noetherian properties of coherent sheaves 35
0.41 Transporter and annihilator ideals 37
0.42 Gap sheaves 37
0.43 Analytically rare sets 38
0.44 Lemma of RITT 40
0.45 Hypersurfaces 42
0.46 Constructible sets 43
Chapter 1. COHERENT SHEAVES
1.1 Complex spaces over S 44
1.2 Cones over S 44
1.3 Projective varieties over S 48
1.4 Linear spaces over S 49
1.5 Linear forms 51
1.6 Duality theorem 51
VI
1.7 Change of base for linear fibre spaces 53
T.8 Vector bundles and locally free sheaves 54
1.9 Projective variety over S associated to a
coherent sheaf 55
1.10 Proper and finite maps 56
1.11 Algebraic characterization of a finite holo-
morphic map 57
1.12 Finite Coherence Theorem 58
1.13 Finite spaces over a Stein space 58
1.14 The analytic spectrum 59
1.15 Main theorem on the analytic spectrum 60
1.16 Higher image sheaves 63
1.17 GRAUERTs proper coherence theorem 64
1.18 REMMERTs proper mapping theorem 64
1.19 Semiproper mapping theorem 65
1.20 Cokernel of a double arrow 66
1.21 Analytic equivalence relations 68
1.22 Canonical factorization of a holomorphic map 68
1.23 Holomorphic maps with connected fibres 70
1.24 Stein factorization 70
1.25 Petrification 72
1.26 Proper equivalence relations 74
Chapter 2. DIFFERENTIAL CALCULUS
2.1 Tangent space of a complex space at a point 77
2.2 Coordinate description of the tangent space 78
2.3 Embedding dimension 79
2.4 Characterization of immersions 79
2.5 Tangent space of a complex space 80
2.6 The Jacobian map of a holomorphic map 81
2.7 Tangent space of a holomorphic map 83
2.8 Tangent space of a direct product 84
2.9 Pfaffian forms and vector fields 84
2.10 Derivations 85
2.11 Restriction of vector fields 89
2.12 A theorem of ROSSI 91
2.13 Corank of a coherent module 93
2.14 Singular locus of a coherent module 95
2.15 Regularity criterion for complex spaces 96
2.16 The singular locus of a reduced complex space 96
2.17 Rank and corank of a holomorphic map 97
2.18 Mersions 99
2.19 Differential characterization of mersions 100
2.20 Holomorphic retractions 102
2.21 Normal space of a holomorphic map 103
2.22 Locally trivial holomorphic maps 106
Appendix. NORMAL AND MAXIMAL COMPLEX SPACES
2.23 The Riemann removable singularity theorems for
manifolds 108
2.24 Weakly holomorphic functions 110
2.25 Universal denominators, non-normal locus 111
2.26 The Normalization Theorem 112
2.27 Removable singularity theorems for normal complex
spaces 118
2-28 Lifting of a holomorphic map to the normalizations 121
2.29 The Maximalization Theorem 122
2.30 Lifting of a holomorphic map to the maximalizations 124
2.31 Characterizations of maximal complex spaces, Graph
Theorem 126
2.32 Stein spaces and finite holomorphic maps 127
VII
Chapter 3. DEGENERACIES AND FLATNESS
3.1 Dimension of a complex space 131
3.2 Finite holomorphic maps 132
3.3 Spreading of a holomorphic map 134
3.4 Semicontinuity of the fibre dimension 134
3.5 Geometric rank and corank 135
3.6 Analyticity of the degeneracy sets 137
3.7 Image of a holomorphic map with constant fibre
dimension 138
3.8 Dimension of the image of a holomorphic map 139
3.9 Open holomorphic maps and dimension formula 142
3.10 143
3.11 Definition of flatness 146
3.12 Algebraic consequences 148
3.13 Flatness of finite holomorphic maps 149
3.14 Flatness criterion of BOURBAKI-GROTHENDIECK 152
3.15 Flatness and change of base 152
3.16 Flatness of a holomorphic map into I 153
3.17 Projections are flat 155
3.18 Non-flat locus and flatification 155
3.19 Flat holomorphic maps are open 156
3.20 Flatness of open holomorphic maps 157
3.21 Regularity criterion for flat holomorphic maps 159
3.2 2 Bad loci of a holomorphic map 160
Chapter 4. MODIFICATIONS AND MEROMORPHIC FUNCTIONS
4.1 a-modifications 162
4.2 Proper modifications, purity of branch loci,
CHOWs lemma 169
4.3 CHOWs Theorem 171
4.4 Meromorphic functions 173
4.5 Graph of a meromorphic function 177
4.6 Meromorphic functions and meromorphic graphs 181
4.7 Theorem of HURWITZ 183
4.8 Extension of meromorphic functions 185
4.9 Meromorphic functions and modifications 186
4.10 Theorem of WEIERSTRASS-SIEGEL-THIMM 188
• • •
|
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| dewey-ones | 515 - Analysis 510 - Mathematics |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
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| id | DE-604.BV002243110 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T15:42:39Z |
| institution | BVB |
| isbn | 3540078576 0387078576 |
| language | English |
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| physical | VII, 201 S. |
| publishDate | 1976 |
| publishDateSearch | 1976 |
| publishDateSort | 1976 |
| publisher | Springer |
| record_format | marc |
| series | Lecture notes in mathematics |
| series2 | Lecture notes in mathematics |
| spelling | Fischer, Gerd 1939- Verfasser (DE-588)128621052 aut Complex analytic geometry Gerd Fischer Berlin [u.a.] Springer 1976 VII, 201 S. txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics 538 Espaces analytiques Espaces fibrés (Mathématiques) Fonctions de plusieurs variables complexes Analytic spaces Fiber spaces (Mathematics) Functions of several complex variables Funktionentheorie (DE-588)4018935-1 gnd rswk-swf Mehrere Variable (DE-588)4277015-4 gnd rswk-swf Funktionentheorie (DE-588)4018935-1 s Mehrere Variable (DE-588)4277015-4 s DE-604 Lecture notes in mathematics 538 (DE-604)BV000676446 538 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001474170&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Fischer, Gerd 1939- Complex analytic geometry Lecture notes in mathematics Espaces analytiques Espaces fibrés (Mathématiques) Fonctions de plusieurs variables complexes Analytic spaces Fiber spaces (Mathematics) Functions of several complex variables Funktionentheorie (DE-588)4018935-1 gnd Mehrere Variable (DE-588)4277015-4 gnd |
| subject_GND | (DE-588)4018935-1 (DE-588)4277015-4 |
| title | Complex analytic geometry |
| title_auth | Complex analytic geometry |
| title_exact_search | Complex analytic geometry |
| title_full | Complex analytic geometry Gerd Fischer |
| title_fullStr | Complex analytic geometry Gerd Fischer |
| title_full_unstemmed | Complex analytic geometry Gerd Fischer |
| title_short | Complex analytic geometry |
| title_sort | complex analytic geometry |
| topic | Espaces analytiques Espaces fibrés (Mathématiques) Fonctions de plusieurs variables complexes Analytic spaces Fiber spaces (Mathematics) Functions of several complex variables Funktionentheorie (DE-588)4018935-1 gnd Mehrere Variable (DE-588)4277015-4 gnd |
| topic_facet | Espaces analytiques Espaces fibrés (Mathématiques) Fonctions de plusieurs variables complexes Analytic spaces Fiber spaces (Mathematics) Functions of several complex variables Funktionentheorie Mehrere Variable |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001474170&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000676446 |
| work_keys_str_mv | AT fischergerd complexanalyticgeometry |