bauer pignatelli kdyt=e=t m apt cpxmfd bed

25
Bauer . - Pignatelli 1821755€ kdyt=E=t M apt cpxmfd . Det M ' infinitesimally rigid # H' ( A , to ( n : holarphictayathudle ) M rigid tell BED deformation .fm f9kT%÷ .ua . . o ¥ UGH at a -401¥ . , .MN " " " M Thul Kodaira - Spencer . [email protected] , 459 I Infiniti si may rigid rigid At : apt cpxmfd.DE#X?YiIfiiIisimafpigia H ' CM , ml o C n hilaphicayat bucket µ rigid I than # ' hefty ¥U→ B defamation of M ( IT submersion , BC wut had , Tito , = Mt I ¥13 , sit THCUIE UKM The C Kodaira Spencer Guin hey ? I ( Momon Kodaira 12457 Tnfiaitisiaef rigid rigid

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Page 1: Bauer Pignatelli kdyt=E=t M apt cpxmfd BED

Bauer . - Pignatelli 1821755€

kdyt=E=t ⑦

M apt cpxmfd .

Det M '

- infinitesimally rigid # H'(A , to( ④ n

: holarphictayathudle )

M rigid⇐ tell →BEDdeformation

.

.fmf9kT%÷.ua . .

o¥ UGH at a -401¥. , .MN

" " " M

Thul Kodaira - Spencer . [email protected],459 I

Infiniti si may rigid ⇒ rigid

At : apt

cpxmfd.DE#X?YiIfiiIisimafpigia⇐ H'

CM , ④ml -

-o

C ④n hilaphicayat bucket

µ rigid I than #' hefty

⇐¥U→

B defamation of M"

( IT submersion , BC wut had, Tito , = Mt

I¥13,

sit THCUIE UKM .

The C Kodaira - Spencer Guin hey ? I

( Momon Kodaira 12457

Tnfiaitisiaef rigid ⇒ rigid

Page 2: Bauer Pignatelli kdyt=E=t M apt cpxmfd BED

Profile KIND ②

Find an example.

of an M which is rigid ,

but H' IN ,ul to C Not easy ? )

Thu C1313183.

itnzs sit Hh 82k .

7- Sn Sheath SurfaceSit . rigid & H' Isn

, a) to'

Questa At . KP.fiFind an example of M which is rigel

hut HYM, into C Not easy

? )

tu CBauer -Pignatelli 81

ttnzs sit 3tn.ae#n :

Isn.

a

: minimal . smthesufaefofgeat.pe/

at H' l Sa,

to dried.

Page 3: Bauer Pignatelli kdyt=E=t M apt cpxmfd BED

06=2%2×2%2,

""¥j'

② C -1 plz "

for ,o3z" Katz

% Epl t's Cece 3.

③ G za -

- Cee

XFGXGCGetc

.

Cz KIT GAME At ftp.ic a' 22h43

Sn - Ha real ofay7¥:*.÷÷¥÷÷÷÷÷÷÷÷÷÷÷÷i÷÷

Page 4: Bauer Pignatelli kdyt=E=t M apt cpxmfd BED

3

M ope cpxmfd .

M -

- I!J Cui ,2T , .

. .Z ;) .

It '

us 's

All Mk N 's a

d.ca#*EfukFekKEn9stz.ktus TO

"It Ui tfaith,

" a "atihdapa.FI#Itf9fayzq④ a = Tu

": ⑦ Tini"

)i

'

tasks .

( R -

mfd9iiiineinii.isaan

I tf autres)

→ 4 i= ? HE 2¥ DEd

em.

④ n valued Con ) fan

Page 5: Bauer Pignatelli kdyt=E=t M apt cpxmfd BED

zits " " 's

④Eiko # ' '

seated £4- Ife , 41=0¥ f- 4 ④µhE Could i

.

"eat

.

- de

Mt - de 342 " Hahn, ,

IFE My 45C -

-tht 3

Kika.fi#akzEkAHx3:&xHe . m KureishiFaik

,

Page 6: Bauer Pignatelli kdyt=E=t M apt cpxmfd BED

Ks equation EfendiX

ao÷⇒¥- H*¥ ,

Ifl

.is#dE4--tfIazpdEhdEn4adEh-gtzYr-EIdE=o

F÷÷:÷÷÷÷¥*ui*i'fzftfzetdz-rndz-h-9adzhnf.IE

f¥I÷radialquean*t÷I!= Sledded a ¥ (4§dEtIz¥= 98 dean jz.IT dead # f¥

t Bidet a egg

desngz.li#idHf59IdEhFE

Page 7: Bauer Pignatelli kdyt=E=t M apt cpxmfd BED

£1 Preliminary [ Mk chapter 4h43 ? ④

Mgm

qq.zrfd.fiHermitian metric .

power)AP :

-

- foam valued CGpl fan } ¥qi¥a¥¥z" " t

Jtf I : = adjoint ofI '

( 4,541=199,41 east .

O : = DI - I 8D Laplacian.

Tut Hodge - Dekha in- Kodaira

.

AD = HIP ⑦ DA "

HIP -

- fee if I 04=032 HMM ,④ n

I.

SSI Kurowski They( Namu - Kadam degrading

M Cpe cpxanfd .

if '

- Heinie im metric .

At i

-

- 5 Utah# Coal fun 3. HAIFA It Ess.

Of It ) :-. In adat"¥¥¥÷¥¥

( ( 4 ,It ) -

- ⑨Rig action 's )

D= JET DI Lapland

Hodge - DeRhun - Kodaira .

Lf = the ⑦ OLE -*

" = seedy oe-oi.IHYM.org

HChamicgenkrh.se

Hati;!:.int{ a LKL t.de

to Eea ? AXE LastE- He t DX tie to 69 .

G .

.

Green agent - Fa, af! y .

Page 8: Bauer Pignatelli kdyt=E=t M apt cpxmfd BED

a. i' ⑥

. H :Charmonic operated : AP -7 HIP pigeon.

the EAP in EAP at 4= Htt04=44-1061.

Hi ' Gfgreen put -I A "

→ AAP

4 I - X

SSI Kurowski They( Namu - Kadam dupe after

M Cpe cpxanfd .

if '

- Heinie in metric .

At i

-

- 5 Utah# Coal fun 3. HAITI # fits.

Of It ) :-. I a adpnt" ± ¥!¥¥¥

( ( 4 ,IX ) -

- ⑨9,4J actor 's )

D= GET DI Lapland

TheHodge - DeKhan - Kodaira .

Lf = the ④

DLE.lt?:=ceeI4oe=oi.IH9fkOedHChamicgenkrl:ea-Htt'T;!::L.

{ a L th t.tn 3It

t 9 Eea ? AXE LastE- He t DX tie to 69 .

G : Green agent Ea → Lat 1- , 69 .

. - X .

Page 9: Bauer Pignatelli kdyt=E=t M apt cpxmfd BED

⑨IH

'

a ONR MI, . . . Md

.

Eh 3. APth¥fEf. .

I .

. . Ed .

¥599412 . EH EFG Eaten M¥44771193M

knit= Ethier. TED

Granet,

4h43,

.

fuk Ihop BiH I Huta "

/tenetsbhEtIE3 .

I ethkhukphiel

(TEED. Flatten ⇒ X= Chiti TEDG Ex X ]( at Hats 4cal -

.a ¥' 2

)is tht 's 4 ,

= EMite

Uncle =

EDGEUx , he

- x ) WEA :L(hence

, :-. Epa xtkt 'd " C 47*221 )

i¥¥h:÷.

'Is :

÷:*. ..¥knife Enid 's Hr RHINE "E2IEhA7EfI

Ece -

- Erie . +IDG Hiked

=¥¥¥* run .

"

ieiiiioee.int:n*÷÷¥÷÷÷÷÷. .

Kate EdG¥Eex.mil( eerie.ca?7enxa3 )Ap Ike - Elect ,

HAH.ec#--o.ntix:i.:::::t:::I

Page 10: Bauer Pignatelli kdyt=E=t M apt cpxmfd BED

The [

MkPwp2iTh3l

⑧C

115pm-

Effy=o⇐ .

Hanft,

-

- o .

H S= See Bet

Hoff#

htt) -

- 03

( o Be cold Be%±hE 's ) c -9kt .

- S : analytic set . fedins ? d- dim

p-

KEES ,htt 1274941? ' Efoffices 's

.

Mf . C-⑦ nrate C ON fun

£4 - IN , 43=0 non .

o

7-F : µ → M differ F-

YES.

s.tn/oF--lffH&FiMx-sMec*bihalarphic

M

the kuwishiH SIFTER I thee ,

@ HI less784 te BE & #at

, # = o t- alt at 1=7112 .

⇒ Niece It Ik FEff Meet IF Made GI 's"

# Its

feekelftf.ee#=o? I THX : Truth . confer "

ayeic set If - Ift ,=o faithful '

-7112.

( :' H'Yasirknee 's.me#ff.feYYa9Yq

. IF : µ - in drffeo EES.

⇐ I C¥eRD=oe*w , # a

S 't Xo F = 941 Et,

F- Me = ,Meat

. bihholaphic

Page 11: Bauer Pignatelli kdyt=E=t M apt cpxmfd BED

c Def Def I '- =fteBelH[ eat .ec =p

.

( Cat 9881

Kunauishifanily

.

"

Pwpe Defa ) I point . ⇒ M rigid .

[ 13465k¥

(###PI Tell -713 deformation

→ 7- XCX CA ⑦ n- valued Call fur .

attire Mata

⇒tee 13I Fdiffeo

,

7- to C-Def . at

F : Mae IMeetbi haloE.,

M .

⇒ tell, Th # EM EF"

M rigid

Gefle k¥6, ]

( T " Attic frherh.lk

infiniti singer:&;DDef H Odin ⇒ M rigid

LEHIHe Defy I point ⇒ M rigid

.

Tell-713 AHHH

DI Def CM ) :-.feefeftcfeceieeet-o.la?xeacoTuk*comfanHkunn-shifntyTY'¥¥tµnY¥x¥!%ee;a***i

( Ren Man Sruthi . Hittite 'm → Categorical 1=2 ' "' '

tutti )

¥&I fdiffeo 7-

to EDM at

F : MEMe .

hi halo

Yy ← Defeat pts⇒ titrate on ⇒ If:*: kindly

Eicher - Givati

Cqinfiutisimctrigiffff.pe/tNttIf-MrigidFIIIH4o

Page 12: Bauer Pignatelli kdyt=E=t M apt cpxmfd BED

i HEGE ④CRPlenty

A It 'lMxNi④nxnl=HYMi④nl④HYM④N)⇒ Detain ) -

- Define )xDetN1( 4mxnH=4nHt4nHH ) )

② GAM G-finite, faithfully actin .

⇒ Def = Detain HYNEKftekelkfkxiectho.GE#kt4 HEEM }

( Detente Be → Hi than .

ti - EYE.

" HIE )

Page 13: Bauer Pignatelli kdyt=E=t M apt cpxmfd BED

theHYMN

, nah -

. H' IN.

.at#H4Yy9nlDeflMxNt--Deffh1xDefNtPwfYmwH=9nH-

Tuft ti 't ' 's.

'

-

'

than..

. Vin , H . . . VEIN

.

HT'm HI -

÷÷÷÷÷÷¥÷÷¥¥÷..⇒U

Page 14: Bauer Pignatelli kdyt=E=t M apt cpxmfd BED

G -

-

finite.

Pups GAM faithfullCftid ⇒

"Ima -told

⇒ Dethklok Deffhlnttluionl .

Vegeta! affect,.ee#f

cnn.kci.ci#TESEEM tepee.ec#=oftFG'fxr=rxsea)

④ Hye -

- Eri - w - IDG Cee.ae#JM-gGinvneerictcnkz-hc.CGfinte

)

Bfg.ie#i.fg*r.it...-IDGG*9.gxB

it

yeaa

"' giiiehe-

- eat ⇒

.

Esprit -

- Grier⇒ Ei rite = ¥ fea ! Aditi

⇒ let 'YM , Ah ,9 at .nu .

ee Defend ⇒ te Defcon.nHYMc④nH

Page 15: Bauer Pignatelli kdyt=E=t M apt cpxmfd BED

at:n±¥¥¥⇒

DetourHKMGHG.aeEH -

. Ether - tweaked"gear gie # = finite - EPG KHAKI

talent. ni gy,

# = Kel . futures)

→ tag geek -Elk ,

→ tEDefHhG . c,

Page 16: Bauer Pignatelli kdyt=E=t M apt cpxmfd BED

② Catanese'sTheorem [ Cat893 ④

2 : Snath put surface . Def - ath

G- - finite . GAZ faithfull.

Asst X = 4g has Duval singularity

QHKVFfhtffdf.gg#fAniDn,Eo.EnEN(-1ane4Y'

" real )then. S→X minimal resolution

.

t - m

Def CSI = Deff x R.

Rtpoiil scheme

( QYG Gas Laal sfntesubgnep)( Duval singularity 4422213912

( An - "

t.IE#..i:.n.iitiiiii*ii.tiiii*Cataneeth

EiEmi::p.

stain .tt#Eihe.

X : 4g has ' DuVal Agility( An

, Dn Ea,

Eiko I

④hen S → X Niuiml resulutiu

,.mn .

ft' ¥.at?h:iRlxkhhf3ta3AalH-&

Page 17: Bauer Pignatelli kdyt=E=t M apt cpxmfd BED

a ' ¥114

[email protected]

"÷¥÷÷÷÷÷÷:W

Page 18: Bauer Pignatelli kdyt=E=t M apt cpxmfd BED

[email protected]

! ' 2%2,52%2,

Thcpksoiirhkl → G11

FELL ,R ?

21-7 Clio )

f 1-7 C Oct )

red- R

I Riemann ext thane

⇐can

. → MAGI:e¥!¥.

Gal> Monodromy . 2=4,01 p

-- Call

f- Hit ) X t's

IN h 't.¥4!!! qai.ua#ees.Bi-ak

' t*ia⇒a** ."i#ITHGH 'nd' ' la :#¥1.99Tu #

tonsil- , G. :

.

. .

Edie >

21 - Chu ,

IEl - I On )

,a

..

: tea ,

*c.ca . - spa,

not:÷9÷!÷ IMohanty

.tl" 2=4,01 f- Cool ) Ht 3

-41 f- '¥n2.lt#4t=c-c, -11

( ÷.

" " " "÷÷¥¥%*¥:* .

i.

Page 19: Bauer Pignatelli kdyt=E=t M apt cpxmfd BED

I ④ga

-

. HE '

#28 " - " 2K¥}x¥I¥

. .!

G -

-

Cz -

-C . 2= Gxcz

.

o

:*=GxG/G

.

SIX

minindresok-HGHaihlr.ieCade) 04,714

= ( ( ahhh ,Catlike )

( dei I -

- Kal -83alliesF C debt =-3 HAE GLC ? Mna ) ht )

GO -

- HEH " 72.

G- Gifzkk I GXG .

f- GXCYG etc . ==o ..

%.ee) : Cia → axe ..

64,94 → Gaceta , #like )

¥- Hal eat Casey ear

( det -

-

- I -14=3×1*93 # ha Yazawin

S - SX nriainl resolution Eft .

I

Page 20: Bauer Pignatelli kdyt=E=t M apt cpxmfd BED

Png XII Gta Aa ' # Duvalsiyulnity.EE.

PI hitmen PEAKY f- in Gp ETHCPI a Echl

f- 2=4×6 → 4=946/9 I'M .

① FC Gp,

G'pl ) a . . uhh ⇒ F- p

'

'

Htt Cd , b)

ftp.glpl) = Cfp ,

Gpl).

⇒ cqht-oety.isPENNE

( Ho , phone . Call 9p=gp ⇒ a =

I * otitis:¥÷÷÷i⇒e.

②. p

-

-

plate.

# Stahl Gp,9ps) = 2

( tailor at - o ⇒ 2h ' ⇒ cash Hojo!!yut-ett.es#2klI.THlp),xTkpAh2--a35V-pE99lis3ae-t

F*¥¥÷i±¥¥¥. .

. -3 X 2 763

Page 21: Bauer Pignatelli kdyt=E=t M apt cpxmfd BED

styuln.ee#Stahlgagp5Fi,④

loalt-IJYA-2hHQYzkze.GRBAI

Page 22: Bauer Pignatelli kdyt=E=t M apt cpxmfd BED

p-

- pl acte

Call @p Gpl ) = Cgo.gr/tffCah7l22slsGn

( 54N "

f- also EH 's

zero ⇒ big:?)fifths . .

p -

. pl.I. " McGinnis

qffp.fpiftddkgp.gptcftxh3PC-fonibf-xk.tt#ah.cgpidp1f-2

*

It .

as .

a ;:

orhiecfa.GG/=zpecfxxh 't

ad

.¥-1 ecuza' "

&a

X2) cuz

loaders Statik 'm 2h. Assiduity

C GY Ss .

' kits : "" )

Page 23: Bauer Pignatelli kdyt=E=t M apt cpxmfd BED

th S is rigid④

Pff①

Def = Detect x Defect② Ditch = Deff , n Hk C. ④4G

Cataneseh= O EHKR, Opt- oDef

= Def Gx R

.

= DefectxD etchHR= ox R ⑦ dim

- s rigid ,

Page 24: Bauer Pignatelli kdyt=E=t M apt cpxmfd BED

The HIS ,

tofix ④

FI , . . Fs - Hicks

If I = EYE' Exception dinars ( Eik -21

1e¥yEthiffH ,- lxisfren

A deniuedfueen .

)

[Huthp-w3 -2 . Exercise )

OT Hoel 'S,

t HOG,→ HES.EE ,

→ HH.IS ,→ Ht CSOs) - i - . .

Hols.EE/EH9X-krxoHOtxHI,H42$cs3iGz)G

-10 C 2,

6=0

Citocko )

!. HHS , ↳ H' CEOs )

Page 25: Bauer Pignatelli kdyt=E=t M apt cpxmfd BED

[Burns - Wahl

94712yd.io/AieI*GaQ

,

HHS,

¥.it#GasHfdit

(food

-

cohomology dy feel # hairdo.

Hie .sc- V →

Spec 'Y¥¥⇒( ..

:÷÷.

:* .)

I.

THIS , Esko

( HH GarrattH