Lectures on resolution of singularities:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Princeton and Oxford
Princeton University Press
2007
|
| Schriftenreihe: | Annals of mathematics studies
number 166 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Literaturverzeichnis: Seite 197 - 202 |
| Beschreibung: | vi, 208 Seiten |
| ISBN: | 0691129223 9780691129228 0691129231 9780691129235 |
Internformat
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| 490 | 1 | |a Annals of mathematics studies |v number 166 | |
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Datensatz im Suchindex
| _version_ | 1804136428098027520 |
|---|---|
| adam_text | Contents
Introduction 1
Chapter 1. Resolution for Curves 5
1.1. Newton s method of rotating rulers 5
1.2. The Riemann surface of an algebraic function 9
1.3. The Albanese method using projections 12
1.4. Normalization using commutative algebra 20
1.5. Infinitely near singularities 26
1.6. Embedded resolution, I: Global methods 32
1.7. Birational transforms of plane curves 35
1.8. Embedded resolution, II: Local methods 44
1.9. Principalization of ideal sheaves 48
1.10. Embedded resolution, III: Maximal contact 51
1.11. Hensel s lemma and the Weierstrass preparation theorem 52
1.12. Extensions of K((t)) and algebroid curves 58
1.13. Blowing up 1 dimensional rings 61
Chapter 2. Resolution for Surfaces 67
2.1. Examples of resolutions 68
2.2. The minimal resolution 73
2.3. The Jungian method 80
2.4. Cyclic quotient singularities 83
2.5. The Albanese method using projections 89
2.6. Resolving double points, char ^2 97
2.7. Embedded resolution using Weierstrass theorem 101
2.8. Review of multiplicities 110
Chapter 3. Strong Resolution in Characteristic Zero 117
3.1. What is a good resolution algorithm? 119
3.2. Examples of resolutions 126
3.3. Statement of the main theorems 134
3.4. Plan of the proof 151
3.5. Birational transforms and marked ideals 159
3.6. The inductive setup of the proof 162
V
vi CONTENTS
3.7. Birational transform of derivatives 167
3.8. Maximal contact and going down 170
3.9. Restriction of derivatives and going up 172
3.10. Uniqueness of maximal contact 178
3.11. Tuning of ideals 183
3.12. Order reduction for ideals 186
3.13. Order reduction for marked ideals 192
Bibliography 197
Index 203
|
| adam_txt |
Contents
Introduction 1
Chapter 1. Resolution for Curves 5
1.1. Newton's method of rotating rulers 5
1.2. The Riemann surface of an algebraic function 9
1.3. The Albanese method using projections 12
1.4. Normalization using commutative algebra 20
1.5. Infinitely near singularities 26
1.6. Embedded resolution, I: Global methods 32
1.7. Birational transforms of plane curves 35
1.8. Embedded resolution, II: Local methods 44
1.9. Principalization of ideal sheaves 48
1.10. Embedded resolution, III: Maximal contact 51
1.11. Hensel's lemma and the Weierstrass preparation theorem 52
1.12. Extensions of K((t)) and algebroid curves 58
1.13. Blowing up 1 dimensional rings 61
Chapter 2. Resolution for Surfaces 67
2.1. Examples of resolutions 68
2.2. The minimal resolution 73
2.3. The Jungian method 80
2.4. Cyclic quotient singularities 83
2.5. The Albanese method using projections 89
2.6. Resolving double points, char ^2 97
2.7. Embedded resolution using Weierstrass' theorem 101
2.8. Review of multiplicities 110
Chapter 3. Strong Resolution in Characteristic Zero 117
3.1. What is a good resolution algorithm? 119
3.2. Examples of resolutions 126
3.3. Statement of the main theorems 134
3.4. Plan of the proof 151
3.5. Birational transforms and marked ideals 159
3.6. The inductive setup of the proof 162
V
vi CONTENTS
3.7. Birational transform of derivatives 167
3.8. Maximal contact and going down 170
3.9. Restriction of derivatives and going up 172
3.10. Uniqueness of maximal contact 178
3.11. Tuning of ideals 183
3.12. Order reduction for ideals 186
3.13. Order reduction for marked ideals 192
Bibliography 197
Index 203 |
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| classification_rvk | SK 240 |
| ctrlnum | (OCoLC)70839833 (DE-599)BVBBV022374304 |
| dewey-full | 516.3/5 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
| dewey-raw | 516.3/5 |
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| discipline | Mathematik |
| discipline_str_mv | Mathematik |
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| id | DE-604.BV022374304 |
| illustrated | Not Illustrated |
| index_date | 2024-07-02T17:08:32Z |
| indexdate | 2024-07-09T20:56:14Z |
| institution | BVB |
| isbn | 0691129223 9780691129228 0691129231 9780691129235 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-015583405 |
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| physical | vi, 208 Seiten |
| publishDate | 2007 |
| publishDateSearch | 2007 |
| publishDateSort | 2007 |
| publisher | Princeton University Press |
| record_format | marc |
| series | Annals of mathematics studies |
| series2 | Annals of mathematics studies |
| spelling | Kollár, János 1956- Verfasser (DE-588)113796277 aut Lectures on resolution of singularities János Kollár Princeton and Oxford Princeton University Press 2007 © 2007 vi, 208 Seiten txt rdacontent n rdamedia nc rdacarrier Annals of mathematics studies number 166 Literaturverzeichnis: Seite 197 - 202 Singularities (Mathematics) Auflösung von Singularitäten (DE-588)4181537-3 gnd rswk-swf Algebraische Fläche (DE-588)4195660-6 gnd rswk-swf Algebraische Kurve (DE-588)4001165-3 gnd rswk-swf Auflösung von Singularitäten (DE-588)4181537-3 s Algebraische Kurve (DE-588)4001165-3 s DE-604 Algebraische Fläche (DE-588)4195660-6 s Erscheint auch als Online-Ausgabe 978-1-4008-2780-0 Annals of mathematics studies number 166 (DE-604)BV000000991 166 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015583405&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Kollár, János 1956- Lectures on resolution of singularities Annals of mathematics studies Singularities (Mathematics) Auflösung von Singularitäten (DE-588)4181537-3 gnd Algebraische Fläche (DE-588)4195660-6 gnd Algebraische Kurve (DE-588)4001165-3 gnd |
| subject_GND | (DE-588)4181537-3 (DE-588)4195660-6 (DE-588)4001165-3 |
| title | Lectures on resolution of singularities |
| title_auth | Lectures on resolution of singularities |
| title_exact_search | Lectures on resolution of singularities |
| title_exact_search_txtP | Lectures on resolution of singularities |
| title_full | Lectures on resolution of singularities János Kollár |
| title_fullStr | Lectures on resolution of singularities János Kollár |
| title_full_unstemmed | Lectures on resolution of singularities János Kollár |
| title_short | Lectures on resolution of singularities |
| title_sort | lectures on resolution of singularities |
| topic | Singularities (Mathematics) Auflösung von Singularitäten (DE-588)4181537-3 gnd Algebraische Fläche (DE-588)4195660-6 gnd Algebraische Kurve (DE-588)4001165-3 gnd |
| topic_facet | Singularities (Mathematics) Auflösung von Singularitäten Algebraische Fläche Algebraische Kurve |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015583405&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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| work_keys_str_mv | AT kollarjanos lecturesonresolutionofsingularities |