tasted- cmJoint we -k with B

. Siebert

( Next talk : examples - l H .A-giiz)

SYZ moti-alien ( Arnoux 's point of view,"

Mir - o- symmetry and T -duality

in the diplomat of an ant' -

canonical divisor ".2007 )

e.g . 1ps I Cine v conic )

#.IF a Lagrangian T2 - f. b- alias ⑧n

B EIR' /Une si- guk - f. b-e :

←22 master index o disks

f. be - ing ore- lies

in trace

⇒ idea : canst--at manor

by d- alizirg the fibration,

- on both sides ! these

cave with tee semi - flat

complex strafe , and then glee using

information from MI o disks . Can do

this by specifying coordinates by country

MI 2 disks with baudry on SYZ f. keg

and save asymptotic behavior

⑥ ←monomial on ma- or a

¥i. t¥¥÷÷÷÷.

More ccuplicated sit- aliens i

-

i¥¥÷÷÷¥÷÷÷÷÷÷±.tch -alien receding whichf. hes ha -e MI o disks

ul bi - - de- y ou takealong with carts.

B -chen lies ( G.

'09 ) PL paths which

are f-picul analogues of MI 2 disks.

(ants of b- chen lines may be used

to define theta f -actions,

and scatteringdrag- am is consistent - f t - functions give

a well - defined gluing of the - a- ie- s pieces.

C. In general , to avoid issues of con- e -genre

ve-U either to all finite orders CGS )

← in the non- Archimedean no- Id (KS ) .

Grrss-ltacking-kee.lk Canonical scattering

diagram in z - din 's .

idea : stet neth a log Ct pair

( X , D) DE l - Kyl cycle of rational

D ,cues ¥zA-%

Bald base of p -take St -2 diag - um

Combinator- cally 1d=a or tropically

cf IX,D) Cen p -t off . @

stroke so hue

sing -Katy at origin"

"

e:"

:c::

A wall is a ray

1RzolaDEtbDitIS.gdLa.bl-1@quippedu.tha teacher

exp ( ¥, kN,tf Eikazi!! )

c- KL-QJLTzi-azif.IT whe - e

Q E Hz ( x) is a monoid curtainingall effective acre classes of X

,

K t Ezo , Npt # of c-- s of

class f meet . -g be . - day at one

point , with contact c- de - s ka,

Kb with

De. Dit, respectively.

( To define ago -o - Sly, used relate GW

tea - y,now use kg Gw teeny. )

-

Higher dank version-

Fix pac - CX ,D)

,

with K×tD a o

( don't need this,

weaker hypotheses s-ff.ee )s

D= ED , sire.

E ='

Assume it IEGI,

. . ;D,

D,:=

,?± Di

es connected . Ass -m also F o - A-at- on,

i - e .,

same DI is o - din 'L.

Bald base B of 54£ f. h -athos

Let Dr-DCXI = g -e- p of divisors spp .-led

on X,basis Dc

,

-

is DS

D- -pl r = It . - Cbiuplxl , IRI .

basis BY, " , Dsk

P = { ¥±Rz.DE/IEE4--.s3st.D+e4}B= U o is pu - e n - d.n'l

op m-d.mx,

let D= U o e B,

B. = BIO-opdin -=n -U

Define affine state on Bo ( 6-5,Lolo,

ma -e

generally,NXY

,

2018 . )For pep

,

din p = n - c , peg fi,dan

. h

" "'

caiman..m¥CHE , - 'Diii CD! . -mins

define embedding

ad → (Rh ( basis er,

- sent

by Dif is Cj on G

bi! rs - en -"

%dDijbsin.in.is) - er

nThes g - es che - Ts Kp : Intl ,q -

T) → N

Sto - Ip)

defining office struts .

The canonical wall St-acte-

'

.

For each

cone -c- P,

d.m • = a c - n - l,

cure class P E Q,

U a non - Ze -o

integral tangent vector to -,

choose a family Tcf tropical cc -ee in B

with universal family of dim. n -L

and with one leg :

A- Cas p - acted gies

•-•↳ a n -mke - NTP,€# associated to ten , data,

¥9 essentially cc - ah -g leg Lp . - clad)Cl - es which tropical ' Ze to

c-s of type c ( or degenerative )

let Pre be the c. din. A cane swept at

by the leg,

teen get craft

( Pe , exp ( Ken PITI?' ) )

c'EI

where o= { RzoDi* 'c' EI

u= { a;D#c' c- I

The collect . - if all s-ch nulls is te

canonical scattering diag-um.

Thm@Th.s scattering diagram is

consistent .

Pf is not difficult : ingredients :

① A pact-ed cue lb - chen hacorrespondence theorem -

② Defamation invariance of GW incarnate.