Quantizations of conical symplectic resolutions:
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| Main Authors: | , , , |
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| Format: | Book |
| Language: | English |
| Published: |
Paris
Société Mathématique de France
2016
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| Series: | Astérisque
384 |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverzeichnis Seite 173-179. - Zusammenfassunen in englischer und französischer Sprache |
| Physical Description: | xii, 179 Seiten |
| ISBN: | 9782856298459 |
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Titel: Quantizations of conical symplectic resolutions
Autor: Braden, Tom
Jahr: 2016
QUANTIZATIONS OF CONICAL SYMPLECTIC RESOLUTIONS Join BRAD FA'. Anthony LICATA, Nicholas PROUDFOOT Ben WEBSTER r m/mmammstM Wmmm M m I mm k wiMm wmmm wsmm mmm mss WMBMi Wimsimm wmmm tmm ?mmm wMmm 'Wmmam wmmmm mm. HMs mmm
TABLE DES MATIÈRES Tom Braden, Nicholas Proudfoot Ben Webster — Quantizations of conical symplectic resolutions I: local and global structure 1 1. Introduction . 2 2. Conical symplectic resolutions . 6 2.1. Deformations . 8 2.2. The Weyl group . 9 2.3. Birational geometry . 10 3. Quantizations . 12 3.1. The period map . 12 3.2. S-structures . 14 3.3. The section ring . 15 3.4. Quantum Hamiltonian reduction . 19 4. Modules over quantizations . 23 4.1. Cotangent bundles . 24 4.2. Localization . 28 4.3. Derived localization . 29 5. Z-algebras . 33 5.1. Quantizations of line bundles . 33 5.2. The quantum homogeneous coordinate ring of X . 37 5.3. Z-algebras and abelian localization . 39 5.4. Comparison of the analytic and algebraic categories . 44 5.5. Twisted modules and the Kirwan functor . 45 6. Convolution and twisting . 50 6.1. Harish-Chandra bimodules . 51 6.2. Characteristic cycles . 56 6.3. Twisting bimodules .
59 6.4. Twisting functors . 63 References . 70
vi TABLE DES MATIERES Tom Braden Anthony Licata Nicholas Proudfoot Ben Webster — Quantizations of conical symplectic resolutions II: category 0 and symplectic duality (with an appendix by I. Losev) 75 1. Introduction . 76 2. Quantizations of conical symplectic resolutions . 82 2.1. Conical symplectic resolutions . 82 2.2. Deformation theory and birational geometry . 83 2.3. Quantizations . 84 2.4. Integrality . 85 2.5. Sheaves of modules . 86 2.6. Localization . 87 2.7. Modules with supports . 88 2.8. Harish-Chandra bimodules and characteristic cycles . 90 3. The categories 0 a and 0 g . 91 3.1. The relative core . 91 3.2. The category Q a . 93 3.3. The category 0 g . 95 4. Categorical preliminaries . 98 4.1. Koszul categories . 98 4.2. Highest weight and standard Koszul categories . 101 5. The structure of 0 a and Q s . 102 5.1. The B algebra . 102 5.2. The category 0 a is highest weight (for most quantizations) . 104 5.3. The category 0 g is highest weight . 107 5.4. The center of the Yoneda algebra of 0 g . 109 6. The Grothendieck group of 0 g
. 110 6.1. Characteristic cycles revisited . 110 6.2. Intersection forms for category Q . Ill 6.3. Supports of simples . 114 7. Categorical filtrations . 117 7.1. Filtration on Harish-Chandra bimodules . 118 7.2. Filtration on category Q . 120 7.3. Relation with the BBD filtration . 121 7.4. The extreme pieces . 124 7.5. Cells . 126 8. Twisting and shuffling functors . 127 8.1. Twisting functors . 127 8.2. Shuffling functors . 129 8.3. Twisting and shuffling commute . 136 9. Examples . 138 9.1. Cotangent bundles of partial flag varieties . 138 9.2. S3-varietics . 140 ASTÉRISQUE M84
TABLE DES MATIÈRES vii 9.3. Hypertoric varieties . 144 9.4. Hilbert schemes on ALE spaces . 146 9.5. Quiver varieties . 148 9.6. Affine Grassmannian slices . 150 10. Symplectic duality . 151 10.1. The definition . 152 10.2. Examples of symplectic dualities . 153 10.2.1. Cotangent bundles of flag varieties . 153 10.2.2. S3-varieties . 154 10.2.3. Hypertoric varieties . 155 10.2.4. Affine type A quiver varieties . 155 10.3. Duality of cones . 157 10.4. Duality of leaf closures and slices . 159 10.5. Duality of leaf filtrations . 160 10.6. Duality of localization algebras . 164 10.7. Knot homologies and symplectic duality . 165 An Ext-vanishing result (appendix by Ivan Losev) . 167 A.l. The proof . 169 References . 173 SOCIÉTÉ MATHÉMATIQUE DE FRANCE 2016 |
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| isbn | 9782856298459 |
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| physical | xii, 179 Seiten |
| publishDate | 2016 |
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| spelling | Quantizations of conical symplectic resolutions Tom Braden, Anthony Licata, Nicholas Proudfoot & Ben Webster Paris Société Mathématique de France 2016 xii, 179 Seiten txt rdacontent n rdamedia nc rdacarrier Astérisque 384 Literaturverzeichnis Seite 173-179. - Zusammenfassunen in englischer und französischer Sprache Braden, Tom (DE-588)1124030883 aut Licata, Anthony (DE-588)1124031081 aut Proudfoot, Nicholas (DE-588)1124399739 aut Webster, Ben (DE-588)112439995X aut Astérisque 384 (DE-604)BV002579439 384 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029419173&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Braden, Tom Licata, Anthony Proudfoot, Nicholas Webster, Ben Quantizations of conical symplectic resolutions Astérisque |
| title | Quantizations of conical symplectic resolutions |
| title_auth | Quantizations of conical symplectic resolutions |
| title_exact_search | Quantizations of conical symplectic resolutions |
| title_full | Quantizations of conical symplectic resolutions Tom Braden, Anthony Licata, Nicholas Proudfoot & Ben Webster |
| title_fullStr | Quantizations of conical symplectic resolutions Tom Braden, Anthony Licata, Nicholas Proudfoot & Ben Webster |
| title_full_unstemmed | Quantizations of conical symplectic resolutions Tom Braden, Anthony Licata, Nicholas Proudfoot & Ben Webster |
| title_short | Quantizations of conical symplectic resolutions |
| title_sort | quantizations of conical symplectic resolutions |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029419173&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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