Topics on real and complex singularities: an introduction
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Braunschweig [u.a.]
Friedr. Vieweg & Sohn
1987
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| Series: | Advanced Lectures in Mathematics
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XVII, 242 Seiten graph. Darst. |
| ISBN: | 3528089997 |
Staff View
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| 245 | 1 | 0 | |a Topics on real and complex singularities |b an introduction |c Alexandru Dimca |
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Record in the Search Index
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| adam_text | TABLE OF CONTENTS
INTRODUCTION
CHAPTER 1: TWO CLASSICAL EXAMPLES: SUBMERSION
THEOREM AND MORSE LEMMA 1
CHAPTER 2: GERMS AND JETS 5
§1. Germs of sets and mappings 5
§2. Basic properties of the algebras En 7
§3. Jets of mappings 12
CHAPTER 3: EQUIVALENCE RELATIONS ON GERMS AND JETS 14
§1. Group actionsand equivalence relations 14
§2. Germs of complex analytic spaces 19
§3. Group actions on jet spaces 27
CHAPTER 4: TANGENT SPACES TO ORBITS 30
§1. Semialgebraic sets 30
§2. Tangent spaces and transversals 34
§3. Tangent spaces to orbits in jet spaces 37
§4. Mather s Lemma 40
CHAPTER 5: BASIC CLASSIFICATION EXAMPLES IN
LINEAR ALGEBRA AND ALGEBRAIC GEOMETRY 43
§1. Linear maps and quadratic forms 43
§2. Cubic forms and plane cubic curves 47
§3. Pencils of quadrics 55
§4. Pencils of binary cubic forms 57
CHAPTER 6: FINITE DETERMINACY OF MAP GERMS 62
§1. R finite determinacy 62
§2. K finite determinacy and isolated
singularities of complete intersections 74
§3. Generic properties of map germs 84
§4. Milnor number and Tjurina number 90
VII
CHAPTER 7: WEIGHTED HOMOGENEOUS SINGULARITIES 99
§1. Weighted homogeneous polynomials and
!E* actions 99
§2. Finitely determined weighted
homogeneous singularities 105
§3. Semi weighted homogeneous singularities 115
§4. Around a theorem of K. Saito 119
§5. Uniqueness of weighted homogeneity
type 124
CHAPTER 8: CLASSIFICATION OF SIMPLE SINGULARITIES
OF FUNCTIONS 128
§1. Simple singularities and adjacency 128
§2. Complete transversals and Splitting Lemma 133
§3. Classification of (( simple function
singularities 136
§4. Classification of R simple function
singularities 144
CHAPTER 9: CLASSIFICATION OF SIMPLE O DIMENSIONAL
COMPLETE INTERSECTIONS 147
§1. Further invariants for singularities:
Boardman symbol and Hilbert Samuel function 147
§2, Normal forms and soecializations 152
CHAPTER 10: CURVE AND SURFACE SINGULARITIES 168
§1. Weierstrass normal form and blowing up 168
§2. Invariants of plane curve singularities 172
§3. Blowing up plane curve singularities 179
§4. Basic facts on resolution of surface
singularities 187
§5. Some properties of simple surface
singularities 192
CHAPTER 11: DUAL MAPPINGS AND CONTACT TANGENCY
CLASSES FOR PROJECTIVE HYPERSURFACES 204
§1. The dual mapping and the dual variety 204
§2. Contact tangency classes 215
VIII
§3. Hyperplane sections of generic hyper
surfaces 220
APPENDIX: TWO RECENT RESEARCH TOPICS 230
REFERENCES 232
LIST OF NOTATIONS 236
INDEX 238
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| indexdate | 2024-07-09T15:43:09Z |
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| isbn | 3528089997 |
| language | English |
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| physical | XVII, 242 Seiten graph. Darst. |
| publishDate | 1987 |
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| publisher | Friedr. Vieweg & Sohn |
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| series2 | Advanced Lectures in Mathematics |
| spelling | Dimca, Alexandru Verfasser aut Topics on real and complex singularities an introduction Alexandru Dimca Braunschweig [u.a.] Friedr. Vieweg & Sohn 1987 XVII, 242 Seiten graph. Darst. txt rdacontent n rdamedia nc rdacarrier Advanced Lectures in Mathematics géométrie algébrique inriac géométrie analytique inriac théorie singularité inriac Singularities (Mathematics) Singularität Mathematik (DE-588)4077459-4 gnd rswk-swf Algebraische Geometrie (DE-588)4001161-6 gnd rswk-swf Singularität Mathematik (DE-588)4077459-4 s Algebraische Geometrie (DE-588)4001161-6 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001493123&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Dimca, Alexandru Topics on real and complex singularities an introduction géométrie algébrique inriac géométrie analytique inriac théorie singularité inriac Singularities (Mathematics) Singularität Mathematik (DE-588)4077459-4 gnd Algebraische Geometrie (DE-588)4001161-6 gnd |
| subject_GND | (DE-588)4077459-4 (DE-588)4001161-6 |
| title | Topics on real and complex singularities an introduction |
| title_auth | Topics on real and complex singularities an introduction |
| title_exact_search | Topics on real and complex singularities an introduction |
| title_full | Topics on real and complex singularities an introduction Alexandru Dimca |
| title_fullStr | Topics on real and complex singularities an introduction Alexandru Dimca |
| title_full_unstemmed | Topics on real and complex singularities an introduction Alexandru Dimca |
| title_short | Topics on real and complex singularities |
| title_sort | topics on real and complex singularities an introduction |
| title_sub | an introduction |
| topic | géométrie algébrique inriac géométrie analytique inriac théorie singularité inriac Singularities (Mathematics) Singularität Mathematik (DE-588)4077459-4 gnd Algebraische Geometrie (DE-588)4001161-6 gnd |
| topic_facet | géométrie algébrique géométrie analytique théorie singularité Singularities (Mathematics) Singularität Mathematik Algebraische Geometrie |
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