tHth676:Dg37

Recall fan ht the tht PICN; it ± Man

This suggests He following conjecture :

Conjectwelltf The Kahler one Kl Mom) f Mom (for n 't 5) is Bomykz to a snbanef

C : = { ( F,

I ) e Ex RI. " " '

" ¥| 0 < es 2 2 min { rj.es

,Ja rebut a 1 set f[n]} ← Psitte • wane

bhe Ct is the one over Tela chamber eating ( 2h, . .

,Et Edam )

.

g-Ddgacheu - Hu

,Pub .

Math .

IHES 871 1998 ),

5-56

A remark uhih I

Kmtfyt thing : think what the

mp PI l n ; i ) → Pol lnir ) uhk fab all khbbs.

The dam is tht for qmicr this

3 an explicit ithtd blew -

up,& for J on a wall K3 is . aposilm f a cavil resdhn f sign bits & an exploit

itrtd blew -

up .

Basialf ,

th . } will be immediate are we identifythe subway tht me getting blown

up .

Wht shed he sottybkmp in Polk ;D ?

sndg the subvarieties f polygons which dgeete at specified collets f edges.

so,

to tht end,

if FED is the

st f all putts f [ is & at FED B f the fom a = IN IN . i.U In

,then dfie Ya to be the

st f all polyps PE Pol( n ; i ) st .the edges e±s

( ' ± she ) are parallel.

f¥ .

with n = 12,8It & a = I,

u IN IN Ia =

,

{ 1,3,

DU { 446 } U [ 5,79 ] U { 8,

' 9123,

a typical demtf ya is

,.

1 2 2

3

1 0 4

98 65

7

In tm.

a gun.

c dht of Poll 12's I ) hdep to Yes 4 p= { Bu { 2} U. . .

u { 123

deaf ,the YBI Polk ; I } ; in gl

,Ya E Pol( k ; :D whets = ( ¥±

,

",

. . .

, Fear i ).

For example,

the fstex . abe

punted to st

1

,.

12 2

3

io 4 →-

c- Poll 4 B)9

8 65

it

Since { D U. . .

U G) ↳ ngpds to the generic n-

gas (& here is in sense the" bisset

..

pretty,

this szggt we shed

mde this a post orderedby reverse refimtjie .

, fr &, Be FID 4 a = IN . . . U In

, p=Jµ ..

.uJm,

we

saya I p D K K s c- m we he Js c- It fr sane Kttk

.

Now we see tht it at P then uhe Ya E Ys . May the 'k are self snothmksra lies a a wall f

smoothed,> ( 2

, D) ; kt in tht are hating a ddgm stet Yi asdty fthedbfr uhih the et,

a

parallel to ooh other ht to no otw edges Indie tht the kdn Jsaf appease Hs. f y; when a- I u Is

btlhse Yahya = single put ,

ahih , tiny a smooth o - mfd )

So then Pokn; i ) = ¥ , →YI is a smooth stntfwtn of Polk; : )

,& the them is :

|hmHI : Assume Pdln ; :) is smooth.

1hm the poplin Folk ; it → Polhill B the itwtdblaopfpdln; :)aby He

propertransform f) all the smooth closed stink in the odrdiektdgthepdnladr an FCD

, strtyfm the

smdht ones.

In genet,if Pollnjr ) is siylr leg .

I = I & n em),

ten it b isolated siyulrity correspondingto line gas whah

,as doomed

abuts are flhe smart stnk

Y±°u±c.

The him is tht the singularities admit anenidresddn,

& here :

|hmH# : Assume Polk; :) is sign.

Then PI ( n ; :) → Pdlnir ) s the capnitefte avid oaths of sins bits f.Had y the

ithtdbbwpsfte really rsoktnalg He pgrtmts f) all otw Foth dvdsktn in the odrdittd J the phd order, stty

fmtusmlht .