Quantization Kohler structures and generalized Work Bischoff Francis with in progress
Based arXiv 1804.05412 our paper : : on . . .
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Summary want potential K Kahler Gen : . Pre ) A Quantization want He , - a geometrical holomorphic input key : Poisson E geometry
' 01 ) to ( TheKoihlerpotenti# Donaldson according I t.in#Ka)=5Aa,AaEr9Ua ) i 25 Ka w = = - Ht #-) - Ap /←ahkrc [ Aap ] holomorphic Aa e Aap = Tie Tq translation Aap Glue by to , using , - , i ⇐ ÷÷÷÷÷ ' I -
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Moritaca-te.org r ) ( X its realizations study Weinstein poisson via symplectic : , i÷ : " i " it - tD¥¥ - • ( Kerth Ttr t IT lnvolutire - - ' ) , 't ) Poisson ( X , ol ' ( X ( x quotient is r • ,
( Weinstein ) 2- category Morita Hr ) - anti ¥ip sp . ' ) Mort I , r 't , X ' x = I x ( xp , • • I e. {4,0×1}=0 Kent '* Ker t* sit i. . ' I 2- it ' ) ft ,r ) ' ' LZ local r isos Mor ) → = , = { § ! ! ! ) µ Picard group Mor Pic ( X r ) . , Weinstein - equivalence self Pic Identity in is distinguished : a grouper 'd .
⇒ " : :::::÷.÷ :* :* T*g Z r scan = = , x Indy ) ( X ' a a o= - - , . , b ) Z a' x ,y I et 2- a a = x , sf It sf It X Ceax , ytxb ) ix. y ) dandlytxb ) dbndx r= -
M.G. , Zab zine ) ( Assuming ' exists ) theorem ( Bischoff QI F = , - ) Kahler structure C g , It , I equivalent A Generalized is CZ , r ) :( . symplectic → txt ,q ) Hot Morita equivalence rt to x. a 's ÷¥ brane with C bisection together nondegenerate a . ' . #t . . It is z - - ( Xt , rt ) ( X f- ) .
. Differ ELE Xt X ÷÷£ . , I L It foliations t induce on s . - . , My real and F • = It Z Is ' " " ' ' ' ' + F' # - F I It = g = - . ( Xt , rt ) ( X f- ) . 't S 'T tensor symmetric unique Riemannian require .
⇒ ⇒ Potential function " ii. art rly read is dry = LU , R ) dk Ke 1mHz ) = n=2i2K dz=r/y=-2i22 ⇒ determined by smooth K function real g .
⇒ x Indy ) :L X. DO ( Z ,r ) ( X ' E a o= - . , , b ) a' ( x ,y eh 2- a a = x , { it :* . if . , dlyntnxeb ) tdlszlrdx r= damn I I I 192 chat 9 Pi Pz Darboux , . 19212 ) { K' Liz ( = 19212 - - - Kohler EZ Gen metric complete . on
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⇒ ⇒ Gutowitfen ( Z w ) ) ( M embed into : r , , n/µ= r ) # sit w . : :;s÷ :* :* :L :3 mis ie . Zee branes M two , Space filling L brane ( brave Lagrangian H=HomlM,Z#T
proposalforquautization-LC.CZ SL ) - model branes A two : in , Imr ) of ( £ Morita brane , equivalence bisection . H=Hom(L,Zcc€
⇒ GK of . ) a p2 Construction ( M , I : { = - HYP ? MT ) 013 ) ) Ho I T E = - study Kainer Fubini Wo = ← 91 at , , ← it i at lenient ← ' o - - Ii ' → Wo ) , it COL TM ) JV =o( sit tr { Cv ,r]=o I ve Hit in . 4 ! ( I " Itt w ( . ) 145 It I = of ds = - a w + = So . fg.It.I-lgeuerahzedkiihleroncp2.se
⇐ construction DO the Iterate ( X. : , , • • 7oz Z -2oz • • - e . , z a . • £12 723 Zoe • • Ly d I d y t a , a , n , X Xz Xo X Xz X , - , z - algebra t-qtO.HomCLoqZ.IT of Lok of Hamiltonian deforms lndep . .
' ) ' ) PG ↳ ( a ) ' ( P for Pic C P Pic IP Mor x = , Ocn ) ) ( 4 , this compute case If in we Ockn ) ) Ho ( IP ' to A Id 4= = • , \ k > o noncommutative Ay Vandenbergh let Id • deformation of A ,
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