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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
[email protected] 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.
[email protected] scattering diagram is
consistent .
Pf is not difficult : ingredients :
① A pact-ed cue lb - chen hacorrespondence theorem -
② Defamation invariance of GW incarnate.