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Titel:	Quantizations of conical symplectic resolutions
Von:	Tom Braden, Anthony Licata, Nicholas Proudfoot & Ben Webster
Person:	Braden, Tom Licata, Anthony Proudfoot, Nicholas Webster, Ben
Hauptverfassende:	Braden, Tom (VerfasserIn), Licata, Anthony (VerfasserIn), Proudfoot, Nicholas (VerfasserIn), Webster, Ben (VerfasserIn)
Format:	Buch
Sprache:	Englisch
Veröffentlicht:	Paris Société Mathématique de France 2016
Schriftenreihe:	Astérisque 384
Notation:	SK 370 SI 832
Medienzugang:	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
Beschreibung:	Literaturverzeichnis Seite 173-179. - Zusammenfassunen in englischer und französischer Sprache
Umfang:	xii, 179 Seiten
ISBN:	9782856298459

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DE-BY-UBR_call_number	80/SI 832-384
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adam_text	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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author	Braden, Tom Licata, Anthony Proudfoot, Nicholas Webster, Ben
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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
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