HOKKAIDO LESSON PISA

Transcription

1 HOKKAIDO - LESSON PISA 3B

2 Here Recll Compct ifi ction Lei Configurtion We will ledwith clssicl ir compct ifictiom wonderful moot configurtion spces will be our nd first exmples Let consider us rel configurtion spce C R = { m n ixm 117 / Exeo iry to } After identifying V = Mph with { n ixm Ex =o } n IR com be seen s essentil complement rel brid rrngement pm in V tht defined hypeylomes rrngement pm me : = He =o { xrxs } for us y re still m V To th set rrngement subsys F pm = { Mifflintown mence { } 4 we m ssocite Mt A H V A = { he = u = following pm % } uth r }}

3 - ' Now we consider Cm k n S V " limitqhe nd following first mp h mens At n SAR where mdunon y on fctor nd nd normltion on projection or fctors n we tke closure imge nd denote y omnnsivkscvhtrpsyt by C Ym mnifold with comers nor obtined

4 \ A picture in xnxx } xy / Expo } I 1123 X1=X3 Xp =Xz n Xz = kg Vf it I = 3=X4 " #±Tkµ* e chmber in picture we see portion S 1123 rrngement S { xzixif fun by 2 pints 5 { xixoxjlt gun by 51

5 chmber Let us consider in 4 R goth tht converges to - zhen to pint its to A form posed in 51 to n l S { x =xz=x3f emerges pths A Lo we home pentgon m picture whose fces re limit points mzing circumference whiusikn nturlly 3 k / = X n z X3= Xy G2 3 :* i f i#xhff 1123! ' 4 iii = 3=Xy

6 forces unsolicited me 1234 by punt hesittions lt Un linen non Mtocihehon ohmenmon Lnmlorly tryout one reohnstion Ltsheff 's 2 tht show com CYM mke by initil from with dimension Mngement We dt H tht on useful m As k re olb " if hs one ounce mnifolds Will vrieties dds 's moth chmber to cnnot mnifold m IR one see boundry oetdmbyos F pm to compute orem Deformtion integrl n btkes ' woe cn omhntoud me for qunttion th subspce rrngement one Ym KONTSEVICH we ech peohttoble instnce Poon C tht fully for one Ltooheff! m notice -2 m corners tht union Concini type : in = Prom given " beutiful bounding wonderful models ' complement IN IP ny PGRM

7 ' Now we consider following picture CYM - SCVK f%!f+ j I PLAY AEFCBM where mp P gmen on every fctor by 2 7 prefect ion Wht imge P Cyn? " IoHAE k

8 mop P 8 1 on vertices on edges 2 1 on fcets P Ym turns out to be smooth rel which on be obtined Iss in following wy vriety We consider embedding IP cm k nd tke closure tht we denote Is IPCY x IT MAY AEF pm by Tm 2hm n exmple rel mod imge 4 compct Concini - We notice tht some construction cn be lone in cse complexities nd we will denote - by Tm 4 corresponding complex model Proi

9 " Zhe vrieties Tm nl In 4 me smooth me obtined ohnn with norml combintoril : dding to p cm k vg crossings whose nd IPCCMCFD 1 irreducible components me boundry by elements F pm indium Y{ toes if D * c- FC pm \{ ok we will represent A by set be he } 2 sme Jen wuhnuble components DA Dq n intersection not empty nd only description if A={ nixes xe } tie { An An } NESTED SET see definition below - Tf intersection not empty n trnsverse Dy nd Dn it smooth

10 " Definition A bet { Be nested set if sets Be Bm } FC Bm Bm me yoiwvme ohsegsint one included one or into 8 set m=1o A = { e 3 } Az= / } {14445/67} nested AwY I*w ffyine %nexaeth * A }= / 134/567 } Ay = As = 1910 } by WE on Hus nested set cn be olerwbeol m leves we dd root ty tree ALWAYS T0 R Tf_ ;

11 - Mumford Zhnefme bounty Tm nd Tm bord by se trees Remrks One omorphm between Mo m+ nd compct fictions : be extended to n 150 between IPCM cn Mon+T Duligne ml Yj C moduli spce genus O stble curves with mte points Lmu on Mqn+T re nturl ction th ction We ction yers on VMT 4 where only n ws eye Aek to going describe n ction bigger symmetric on bns group re H even cohomology YJ Smn Sm

12 We Desuiytion bns Yenul obsuiytions home = been proposed in one tht res nturlly from Wnknful moobl De Concini Tenet Pro cohomology 14 me interested construction teeny z ± zc ± where s me cj Chern losses skip ohms D or c Ht TI e En4 2 we ebrigtwn idol 2henem_ Ywtnmki 6 A born H* Fn 1421 pointed buggy monomil i ck CAM where

13 1 { Ae Are } nested set refore if re cn be represented by forest th not not we ob not "5? 2 mol it t go noblitt 2h 's mens in pntiuln < / Fthnknftmthite / vertex Ag tht number edges tht vote must be from n internl z } town bkonyle m = NATAN or A } you 2 Act You 2 Ay Az A 3 Uvufou th bns H*yTC ZD A 4 referentil by wweightehfnesto 6 89 K

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