Blowing up of non-commutative smooth surfaces:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, RI
AMS
2001
|
| Series: | Memoirs of the American Mathematical Society
734 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Volume 154, Number 734 (end of volume) |
| Physical Description: | IX, 140 S. |
| ISBN: | 0821827545 |
Staff View
MARC
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Record in the Search Index
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| adam_text | Contents
Chapter 1. Introduction 1
1.1. Motivation 1
1.2. Construction 3
1.3. General properties 5
1.4. Non commutative Del Pezzo surfaces 6
1.5. Exceptional simple objects 6
1.6. Non commutative cubic surfaces 7
1.7. Acknowledgement 7
Chapter 2. Preliminaries on category theory 8
Chapter 3. Non commutative geometry 10
3.1. Bimodules 10
3.2. Graded modules, bimodules and algebras 18
3.3. Quotients of the identity functor 19
3.4. Ideals in the identity functor 22
3.5. Quasi schemes 26
3.6. Divisors 28
3.7. Proj 29
3.8. Condition x and cohomological dimension 32
3.9. Higher inverse images 39
3.10. Algebras which are strongly graded modulo a Serre subcategory 40
3.11. The positive part of certain graded algebras. 41
3.12. Veronese subalgebras 42
Chapter 4. Pseudo compact rings 44
Chapter 5. Cohen Macaulay curves embedded in quasi schemes 53
5.1. Preliminaries 53
5.2. Some computations 57
5.3. Completion of objects in mod(X) 60
5.4. Completion of bimodules 61
5.5. The category C/,p 64
5.6. Completion of algebras 68
5.7. Multiplicities in the case that r has infinite order 69
Chapter 6. Blowing up a point on a commutative divisor 72
6.1. Some ideals 72
6.2. Some Rees algebras 76
6.3. Definition of blowing up 77
6.4. The normal bundle 79
vii
viii CONTENTS
6.5. Birationality 80
6.6. The exceptional curve 82
6.7. The structure of the exceptional curve 84
6.8. The strict transform 88
6.9. A result on Ko of some categories 91
Chapter 7. Derived categories 93
7.1. Generalities 93
7.2. Admissible compositions of morphisms between quasi schemes 93
Chapter 8. The derived category of a non commutative blowup 96
8.1. The formalism of semi orthogonal decompositions 96
8.2. Generalities 97
8.3. Computation of some derived functors 98
8.4. The main theorem 101
Chapter 9. Some results on graded algebras and their sections 105
9.1. Generalities 105
9.2. The case of a blowing up 111
Chapter 10. Quantum plane geometry 113
10.1. Multiplicities of some objects 113
10.2. Classification of lines and conies 118
Chapter 11. Blowing up n points in an elliptic quantum plane 121
11.1. Derived categories 121
11.2. Exceptional simple objects 126
Chapter 12. Non commutative cubic surfaces 129
Appendix A. Two categories 132
Appendix B. Summary of notations 135
Appendix C. Index of terminology 138
Bibliography 139
|
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| id | DE-604.BV013945535 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:54:51Z |
| institution | BVB |
| isbn | 0821827545 |
| language | English |
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| physical | IX, 140 S. |
| publishDate | 2001 |
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| series | Memoirs of the American Mathematical Society |
| series2 | Memoirs of the American Mathematical Society |
| spelling | Van den Bergh, Michel 1960- Verfasser (DE-588)134166949 aut Blowing up of non-commutative smooth surfaces Michel Van den Bergh Providence, RI AMS 2001 IX, 140 S. txt rdacontent n rdamedia nc rdacarrier Memoirs of the American Mathematical Society 734 Volume 154, Number 734 (end of volume) Blowing up (DE-588)4508027-6 gnd rswk-swf Nichtkommutative Differentialgeometrie (DE-588)4311174-9 gnd rswk-swf Nichtkommutative Differentialgeometrie (DE-588)4311174-9 s Blowing up (DE-588)4508027-6 s DE-604 Memoirs of the American Mathematical Society 734 (DE-604)BV008000141 734 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009542326&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Van den Bergh, Michel 1960- Blowing up of non-commutative smooth surfaces Memoirs of the American Mathematical Society Blowing up (DE-588)4508027-6 gnd Nichtkommutative Differentialgeometrie (DE-588)4311174-9 gnd |
| subject_GND | (DE-588)4508027-6 (DE-588)4311174-9 |
| title | Blowing up of non-commutative smooth surfaces |
| title_auth | Blowing up of non-commutative smooth surfaces |
| title_exact_search | Blowing up of non-commutative smooth surfaces |
| title_full | Blowing up of non-commutative smooth surfaces Michel Van den Bergh |
| title_fullStr | Blowing up of non-commutative smooth surfaces Michel Van den Bergh |
| title_full_unstemmed | Blowing up of non-commutative smooth surfaces Michel Van den Bergh |
| title_short | Blowing up of non-commutative smooth surfaces |
| title_sort | blowing up of non commutative smooth surfaces |
| topic | Blowing up (DE-588)4508027-6 gnd Nichtkommutative Differentialgeometrie (DE-588)4311174-9 gnd |
| topic_facet | Blowing up Nichtkommutative Differentialgeometrie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009542326&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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