Functions of several complex variables and their singularities:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English German |
| Published: |
Providence, RI
American Math. Soc.
2007
|
| Series: | Graduate studies in mathematics
83 |
| Subjects: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017055758&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Item Description: | Includes bibliographical references (p. 303-306) and index |
| Physical Description: | XVII, 312 S. graph. Darst. 27 cm |
| ISBN: | 9780821833193 0821833197 |
Staff View
MARC
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| 240 | 1 | 0 | |a Funktionentheorie, Differentialtopologie und Singularitäten |
| 245 | 1 | 0 | |a Functions of several complex variables and their singularities |c Wolfgang Ebeling |
| 264 | 1 | |a Providence, RI |b American Math. Soc. |c 2007 | |
| 300 | |a XVII, 312 S. |b graph. Darst. |c 27 cm | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Graduate studies in mathematics |v 83 | |
| 500 | |a Includes bibliographical references (p. 303-306) and index | ||
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| 650 | 4 | |a Fonctions de plusieurs variables complexes | |
| 650 | 7 | |a Singulariteiten |2 gtt | |
| 650 | 4 | |a Singularités (Mathématiques) | |
| 650 | 7 | |a Topologie |2 gtt | |
| 650 | 4 | |a Functions of several complex variables | |
| 650 | 4 | |a Singularities (Mathematics) | |
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Record in the Search Index
| _version_ | 1821381670033424384 |
|---|---|
| adam_text |
Contents
Foreword to the English translation
ix
Introduction
xi
List of figures
xiii
List of tables
xvii
Chapter
1.
Riemann surfaces
1
§1.1.
Riemann surfaces
1
§1.2.
Homotopy of paths, fundamental groups
9
§1.3.
Coverings
13
§1.4.
Analytic continuation
24
§1.5.
Branched meromorphic continuation
29
§1.6.
The Riemann surface of an algebraic function
33
§1.7.
Puiseux expansion
40
§1.8.
The Riemann sphere
41
Chapter
2.
Holomorphic functions of several variables
43
§2.1.
Holomorphic functions of several variables
43
§2.2.
Holomorphic maps and the implicit function theorem
57
§2.3.
Local rings of holomorphic functions
60
§2.4.
The
Weierstrass
preparation theorem
63
§2.5.
Analytic sets
74
§2.6.
Analytic set germs
76
§2.7.
Regular and singular points of analytic sets
84
vi
Contents
§2.8.
Map germs and homomorphisms of analytic algebras
89
§2.9.
The generalized
Weierstrass
preparation theorem
96
§2.10.
The dimension of an analytic set germ
101
§2.11.
Elimination theory for analytic sets
109
Chapter
3.
Isolated singularities of holomorphic functions
113
§3.1.
Differentiable manifolds
113
§3.2.
Tangent bundles and vector fields
119
§3.3.
Transversality
125
§3.4.
Lie groups
127
§3.5.
Complex manifolds
134
§3.6.
Isolated critical points
140
§3.7.
The universal unfolding
144
§3.8.
Modifications
149
§3.9.
Finitely determined function germs
158
§3.10.
Classification of simple singularities
165
§3.11.
Real morsifications of the simple curve singularities
171
Chapter
4.
Fundamentals of differential topology
181
§4.1.
Differentiable manifolds with boundary
181
§4.2.
Riemannian metric and orientation
183
§4.3.
The
Ehresmann fibration
theorem
186
§4.4.
The holonomy group of a differentiable fiber bundle
189
§4.5.
Singular homology groups
194
§4.6.
Intersection numbers
200
§4.7.
Linking numbers
209
§4.8.
The braid group
211
§4.9.
The homotopy sequence of a differentiable fiber bundle
214
Chapter
5.
Topology of singularities
223
§5.1.
Monodromy and variation
223
§5.2.
Monodromy group and vanishing cycles
226
§5.3.
The Picard-Lefschetz theorem
229
§5.4.
The Milnor fibration
238
§5.5.
Intersection matrix and Coxeter-Dynkin diagram
249
§5.6.
Classical monodromy, variation, and the
Seifert form 252
§5.7.
The action of the braid group
259
Contents
vii
§5.8.
Monodromy group and vanishing lattice
269
§5.9.
Deformation
277
§5.10.
Polar curves and Coxeter-Dynkin diagrams
283
§5.11.
Unimodal singularities
292
§5.12.
The monodromy groups of the isolated hypersurface
singularities
298
Bibliography
303
Index
307 |
| any_adam_object | 1 |
| author | Ebeling, Wolfgang 1951-2025 |
| author_GND | (DE-588)141552123 |
| author_facet | Ebeling, Wolfgang 1951-2025 |
| author_role | aut |
| author_sort | Ebeling, Wolfgang 1951-2025 |
| author_variant | w e we |
| building | Verbundindex |
| bvnumber | BV035250095 |
| callnumber-first | Q - Science |
| callnumber-label | QA331 |
| callnumber-raw | QA331 |
| callnumber-search | QA331 |
| callnumber-sort | QA 3331 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 350 |
| ctrlnum | (OCoLC)84838946 (DE-599)BVBBV035250095 |
| dewey-full | 515/.94 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515/.94 |
| dewey-search | 515/.94 |
| dewey-sort | 3515 294 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV035250095 |
| illustrated | Illustrated |
| indexdate | 2025-01-16T05:21:58Z |
| institution | BVB |
| isbn | 9780821833193 0821833197 |
| language | English German |
| lccn | 2007060745 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-017055758 |
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| owner_facet | DE-703 DE-83 DE-824 DE-19 DE-BY-UBM |
| physical | XVII, 312 S. graph. Darst. 27 cm |
| publishDate | 2007 |
| publishDateSearch | 2007 |
| publishDateSort | 2007 |
| publisher | American Math. Soc. |
| record_format | marc |
| series | Graduate studies in mathematics |
| series2 | Graduate studies in mathematics |
| spelling | Ebeling, Wolfgang 1951-2025 Verfasser (DE-588)141552123 aut Funktionentheorie, Differentialtopologie und Singularitäten Functions of several complex variables and their singularities Wolfgang Ebeling Providence, RI American Math. Soc. 2007 XVII, 312 S. graph. Darst. 27 cm txt rdacontent n rdamedia nc rdacarrier Graduate studies in mathematics 83 Includes bibliographical references (p. 303-306) and index Complexe variabelen gtt Fonctions de plusieurs variables complexes Singulariteiten gtt Singularités (Mathématiques) Topologie gtt Functions of several complex variables Singularities (Mathematics) Riemannsche Fläche (DE-588)4049991-1 gnd rswk-swf Singularität Mathematik (DE-588)4077459-4 gnd rswk-swf Differentialtopologie (DE-588)4012255-4 gnd rswk-swf Funktionentheorie (DE-588)4018935-1 gnd rswk-swf Mehrere Variable (DE-588)4277015-4 gnd rswk-swf Funktionentheorie (DE-588)4018935-1 s Differentialtopologie (DE-588)4012255-4 s Singularität Mathematik (DE-588)4077459-4 s DE-604 Mehrere Variable (DE-588)4277015-4 s 1\p DE-604 Riemannsche Fläche (DE-588)4049991-1 s 2\p DE-604 Graduate studies in mathematics 83 (DE-604)BV009739289 83 Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017055758&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Ebeling, Wolfgang 1951-2025 Functions of several complex variables and their singularities Graduate studies in mathematics Complexe variabelen gtt Fonctions de plusieurs variables complexes Singulariteiten gtt Singularités (Mathématiques) Topologie gtt Functions of several complex variables Singularities (Mathematics) Riemannsche Fläche (DE-588)4049991-1 gnd Singularität Mathematik (DE-588)4077459-4 gnd Differentialtopologie (DE-588)4012255-4 gnd Funktionentheorie (DE-588)4018935-1 gnd Mehrere Variable (DE-588)4277015-4 gnd |
| subject_GND | (DE-588)4049991-1 (DE-588)4077459-4 (DE-588)4012255-4 (DE-588)4018935-1 (DE-588)4277015-4 |
| title | Functions of several complex variables and their singularities |
| title_alt | Funktionentheorie, Differentialtopologie und Singularitäten |
| title_auth | Functions of several complex variables and their singularities |
| title_exact_search | Functions of several complex variables and their singularities |
| title_full | Functions of several complex variables and their singularities Wolfgang Ebeling |
| title_fullStr | Functions of several complex variables and their singularities Wolfgang Ebeling |
| title_full_unstemmed | Functions of several complex variables and their singularities Wolfgang Ebeling |
| title_short | Functions of several complex variables and their singularities |
| title_sort | functions of several complex variables and their singularities |
| topic | Complexe variabelen gtt Fonctions de plusieurs variables complexes Singulariteiten gtt Singularités (Mathématiques) Topologie gtt Functions of several complex variables Singularities (Mathematics) Riemannsche Fläche (DE-588)4049991-1 gnd Singularität Mathematik (DE-588)4077459-4 gnd Differentialtopologie (DE-588)4012255-4 gnd Funktionentheorie (DE-588)4018935-1 gnd Mehrere Variable (DE-588)4277015-4 gnd |
| topic_facet | Complexe variabelen Fonctions de plusieurs variables complexes Singulariteiten Singularités (Mathématiques) Topologie Functions of several complex variables Singularities (Mathematics) Riemannsche Fläche Singularität Mathematik Differentialtopologie Funktionentheorie Mehrere Variable |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017055758&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV009739289 |
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