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 .