Download - Sigma model e Theory - Virginia Tech
The logarithmic gauged linear
Sigma modele Theory
Joint work with Felix Janda
Yongbin Ruan
Adrien Sauvaget
Input on CWsidex smooth prooj varietyIDMstack e.g Ip
v b Ix e.g V 0h52p't
w c How s t Y Ako CXsmooth of codimYx rkV
W n V a st Y dw o
eex E w action
mm R chargec Po V W EE
Rink in Ipo needs not to be V b2 Ipo can't be proper
stable maps with p fields
nodal curve
no markings forsimplicity
fuglieing ive we owEI
Pox w c ew PII J f map with p field
Igp field
f Cls x PCHTf V we
f stable if h is stable
f RLS M instanton moduliMP f C PE stableU
e INDy
I
UVK.cdw.gg
P o
u NP has G w action
2 It recovers CW of Y w oj
Kien Li cosection localization
MP c A NYS
rely on upoW EEs t Ca XP hey rir
2
b Guido NP rely on up EI
Chang Li Kim oh Chang A L
C J Webb R Picciotto
es MP is non proper
We fix this
The RS CJR
There is a compactification
XP c upsit
1 UP is propyer Dan with 6 action
2 3 vis Cycles
up upred upyup
red
depend ondepend on
poop E w Pkp Ciw W
s.t a MP up red
Cbs upVir
upJed m upbupyred
m order of poles of W along co Flpo
How do we compactify MP
How to construct the reduced theory
FLO use stable log maps ofAbramovich C Gross Sierber
1 Poc Ip 2 QIc 11 as a log varietyW c PCV G co
2 Pc i P hq
j J f IvymapClog curve
s
stability f representable
why jtf f Hk f as o
for Ks o I Hs o
Hi ample class on X
Wc at
Fordprinciplizationof piPlµP
UP f jyp5 I
log Rmaps logRmapswith specialconfiguration
Kiem Li coseetion extends to UPIMPnicely non degenerate
poleof order poleof orderof W alongs
up red