
vivekpurna anuman

beejganitiya jyaamiti mein, vivekpurna anuman vakron key moduli sthaan parr sthir vargon kii pratichhedan sankhya key baare mein ack anuman haye, jise kagaj mein edward witton dwara pesh kiya gayaa haye, aur saamaanyikrit kiya gayaa haye. 
vitten kaa mool anuman pepper mein adhikatam kontsevic dwara saabit kiya gayaa thaa. 
anuman key liye vitten kii prerana yeh thee kii 2-ayami quantum gurutvaakarshan key dou alag-alag models mein ack hii vibhajan kaary honah chaahiye. inmein seey ack model key liye vibhajan kaary koo beejganitiya vakron key moduli stack parr pratichhedan sankhyaon key sandarbh mein varnit kiya jaa sakata haye, aur dusare key liye vibhajan kaary key. dee. vee. padanukram key τ-kaary kaa logrithm haye. inn vibhajan karyon kii pehchaan karane seey yeh anuman lagata haye kii pratichhedan sankhyaon seey baney ack nishchit utpann karane vaale kaary koo key. dee. vee. padanukram key vibhedak samikaranon koo santusht karna chaahiye.
bayaan.
maan leejiye kii "m" g "," n "" n "vishisht chihnit binduon" x "1 key saath genus" g "kii compact reman satahon kaa moduli dher haye.., x" "n", 
aur "jee", "aine" iska dilligne-mumford compactfication haye. aine" line bundles "ell" aaee "hain 
"jee," "aine", "jiska fiber moduli stack key ack bindu parr ack reeman satah key cottangent sthaan dwara chihnit bindu" "x" "i parr diyaa jaataa haye. pratichhedan soochkaank τ "d" 1,..., τ "d" n "Â kaa pratichhedan soochkaank haye π" c "1 (" l "i") "d" i "" parr "g", "n" jahaan σ "d" i "= mund" g "," n "= 3" g "-3 +" n ", aur 0 yadi aisaa koee" g "maujood naheen haye, jahaan" c "1 ack rekha bundle kaa pahala cheran varg haye. vitten kaa utpann karane vaalaa kaary
sabhi pratichhedan soochkaankon koo isake gunank key roop mein kootbaddh kartaa haye. 
vitten key anuman mein kahaa gayaa haye kii vibhajan falan "z" = exp "f" kdv padanukram key liye ack τ-falan haye, dusare shabdon mein yeh virasoro beejganit key aadhar sootra _ 2 key anuroop aanshik vibhedak samikaranon kii ack nishchit shrinkhala koo santusht kartaa haye.
pramaan.
kontsevic ney ribbon graph key sandarbh mein moduli rikt sthaan key ack sanyojan vivaran kaa upayog kiya taaki yeh dikhaaya jaa sakey kii 
yahaan daaeen or kaa yog "g" g ", ribbon graph" x "key" n "key samooh parr haye, joe" g "genus kii compact reman satahon key" n "chihnit binduon key saath haye. ee" kinaaron key samooh aur "aiks" key binduon koo "aiks" 0 aur "aiks" 1 dwara darshaaya jaataa haye. falan λ koo chihnit binduon seey vaastavik taka ack falan key roop mein maanaa jaataa haye, aur kinare key pratyek taraf key anuroop dou chihnit binduon parr λ key yog key barabar ack kinare key λ koo sett karke ribbon graph key kinaaron taka vistaarit kiya jaataa haye. 
fenman aarekh takneekon seey, iska tatparya haye kii 
"f" ("t" 0..) ack asymptotic vistaar haye 
jaisa kii λ anant koo udhaar detaa haye, jahan λ aur χ sakaratmak nishchit "n" dwara "n" hermician matricks hain, aur "t" i "dwara diyaa jaataa haye
aur sakaratmak nishchit hermician matricks parr sambhavana maap microne dwara diyaa jaataa haye 
jahan "c" λ ack saamaanyikaran sthiraank haye. iss upaay mein yeh guna haye kii
jiska tatparya haye kii fenman aarekh key sandarbh mein iska vistaar ribbon graph key sandarbh mein "aff" key liye abhivyakti haye. 
isase unhone anuman lagaaya kii key. dee. vee. padanukram key liye aiks. pee. aff. ack τ-kaary haye, iss prakaar yeh vivek kaa anuman saabit hotaa haye.
saamaanyikaran.
vitten anuman hamiltonian pee. dee. ee. kii samaakalansheel pranaliyon aur 2dee topological kshetra siddhanton key kuchh parivaaron kii jyaamiti (kontevic aur mainin dwara tathaakathit samasthaanik kshetra siddhanton key roop mein swayamsiddh) key beach adhik samanya sambandh kaa ack vishesh mamla haye, jiska bee dwara vyavasthit roop seey anveshan aur adhyayan kiya gayaa thaa. dubrovin aur vaaee. jhaang, aeye. diye gaye, see. teleman aur anya.
virasoro anuman vivekpurna anuman kaa ack saamaanyikaran haye.

