Bergman Kernels and symplectic reduction:
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Paris
2008
|
| Series: | Astérisque
318 |
| Subjects: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017016177&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Physical Description: | VIII, 154 S. |
| ISBN: | 9782856292556 |
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Record in the Search Index
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|---|---|
| adam_text | Titel: Bergman Kernels and symplectic reduction
Autor: Ma, Xiaonan
Jahr: 2008
CONTENTS
0. Introduction ..............................................................................................................................1
1. Connections and Laplacians
associated to a principal bundle ................................................................................15
1.1. Connections associated to a principal bundle ........................................................15
1.2. Curvatures and Laplacians associated to a principal bundle ..........................17
2. G-invariant Bergman kernels ......................................................................21
2.1. Casimir operator ................................................................................................................22
2.2. Spinc Dirac operator ........................................................................................................23
2.3. G-invariant Bergman kernel ..........................................................................................25
2.4. Localization of the problem and proof of Theorem 0.1 ......................................27
2.5. Induced operator on U/G ..............................................................................................32
2.6. Rescaling and a Taylor expansion of the operator 4 £p4 -1 ............................33
2.7. Uniform estimate on the G-invariant Bergman kernel ......................................41
2.8. Evaluation of Jr?u ..............................................................................................................53
2.9. Proof of Theorem 0.2 ........................................................................................................54
3. Evaluation of ..................................................................................................................57
3.1. Spectrum of _^2° ..................................................................................................................^
3.2. Evaluation of P^: a proof of (0.12) and (0.13) ..................................................60
3.3. A formula for 0 ................................................................................................................62
3.4. Example (CP1,2 lofs) ......................................................................................................67
4. Applications ..............................................................................................................................71
4.1. Orbifold case ........................................................................................................................71
4.2. tf-weight Bergman kernel on AT ....................................................................................74
4.3. Averaging the Bergman kernel; a direct proof of (0.15) and (0.16) ............76
4.4. Berezin-Toeplitz quantization ......................................................................................79
4.5. Toeplitz operators on Xq ..............................................................................................85
4.6. Generalization to non-compact manifolds ..............................................................90
viii CONTENTS
4.7. Relation 011 the Bergman kernel on Xc ................................. 92
5. Computing the coefficient $1 ............................................ 95
5.1. The second fundamental form of P ...................................... 96
5.2. The operators 0 , O2 in (2.102) ......................................... 98
5.3. Computation of the coefficient .......................................112
5.4. Final computations: the proof of Theorem 0.6 ..........................122
5.5. Coefficient I i: general case .............................................124
6. The coefficient P^(0, 0) ..................................................127
6.1. The terms ^li3, ii;4 ...............................................127
6.2. The term ^ii2 ...........................................................132
6.3. Proof of Theorem 0.7 ....................................................145
7. Bergman kernel and
geometric quantization ...................................................147
Bibliography ..................................................................149
Index ..........................................................................153
ASTfcRtSQUK 318
|
| any_adam_object | 1 |
| author | Ma, Xiaonan Zhang, Weiping |
| author_facet | Ma, Xiaonan Zhang, Weiping |
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| ctrlnum | (OCoLC)297127521 (DE-599)BVBBV035209939 |
| discipline | Mathematik |
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| id | DE-604.BV035209939 |
| illustrated | Not Illustrated |
| indexdate | 2024-12-20T13:25:57Z |
| institution | BVB |
| isbn | 9782856292556 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-017016177 |
| oclc_num | 297127521 |
| open_access_boolean | |
| owner | DE-19 DE-BY-UBM DE-824 DE-29T DE-384 DE-83 DE-11 DE-188 DE-355 DE-BY-UBR |
| owner_facet | DE-19 DE-BY-UBM DE-824 DE-29T DE-384 DE-83 DE-11 DE-188 DE-355 DE-BY-UBR |
| physical | VIII, 154 S. |
| publishDate | 2008 |
| publishDateSearch | 2008 |
| publishDateSort | 2008 |
| record_format | marc |
| series | Astérisque |
| series2 | Astérisque |
| spellingShingle | Ma, Xiaonan Zhang, Weiping Bergman Kernels and symplectic reduction Astérisque Análise global larpcal Bergman kernel functions Index theory (Mathematics) Symplectic manifolds Variational inequalities (Mathematics) Bergman-Kernfunktion (DE-588)4236138-2 gnd Symplektische Mannigfaltigkeit (DE-588)4290704-4 gnd Dirac-Operator (DE-588)4150118-4 gnd |
| subject_GND | (DE-588)4236138-2 (DE-588)4290704-4 (DE-588)4150118-4 |
| title | Bergman Kernels and symplectic reduction |
| title_auth | Bergman Kernels and symplectic reduction |
| title_exact_search | Bergman Kernels and symplectic reduction |
| title_full | Bergman Kernels and symplectic reduction Xiaonan Ma ; Weiping Zhang |
| title_fullStr | Bergman Kernels and symplectic reduction Xiaonan Ma ; Weiping Zhang |
| title_full_unstemmed | Bergman Kernels and symplectic reduction Xiaonan Ma ; Weiping Zhang |
| title_short | Bergman Kernels and symplectic reduction |
| title_sort | bergman kernels and symplectic reduction |
| topic | Análise global larpcal Bergman kernel functions Index theory (Mathematics) Symplectic manifolds Variational inequalities (Mathematics) Bergman-Kernfunktion (DE-588)4236138-2 gnd Symplektische Mannigfaltigkeit (DE-588)4290704-4 gnd Dirac-Operator (DE-588)4150118-4 gnd |
| topic_facet | Análise global Bergman kernel functions Index theory (Mathematics) Symplectic manifolds Variational inequalities (Mathematics) Bergman-Kernfunktion Symplektische Mannigfaltigkeit Dirac-Operator |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017016177&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV002579439 |
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