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cmcsc10AGeneraliza32tionofMumford'sQkGeometricInvariantTheor32y -
cmcsc10JM*urgenHauseny,|{Y cmr8ReceivÎed: AugustX10,2001OfCommÎunicatedXbyThomasPeternell"ō Abstract.]W*eTgeneralizeMumford'sconstructionofgoGodTquotients for(reductivegroupactions.Replacingasinglelinearizedinvertible sheaf1withacertaingroupofsheaves,we1obtainaGeometricInvqariant TheoryproGducingnotonlythequasipro 8jectivequotientspaces,:]but morehgenerallyalldivisorialones.Asanapplication,m}wecharacterize intermsoftheW*eylgroupofamaximaltorus,%$whenapropGerreduc- tive&groupactiononasmoGothcomplexvqarietyadmitsanalgebraic vqarietyUUasorbitspace. 2000UUMathematicsSub 8jectClassication:q14L24,14L30 KeywordsKAandPhrases:lGeometricInvqariantTheory*,MEgoGodKAquotients, reductiveUUgroupactions IntroductionBLetܙthereductivegroup
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