资源描述：
《a note on the super krichever mapnew》由会员上传分享，免费在线阅读，更多相关内容在教育资源-天天文库。
1、Ref.SISSA36/2000/FMAnoteonthesuperKrichevermapGregorioFalqui,CesareReinaandAlessandroZampaSISSA,ViaBeirut2/4,I-34014Trieste,ItalyE–mail:falqui@sissa.it,reina@sissa.it,zampa@fm.sissa.itAbstract.WeconsiderthegeometricalaspectsoftheKrichevermapinthecontextofJ
2、acobianSuperKPhierarchy.WeusetherepresentationofthehierarchybasedontheFa`adiBrunorecursionrelations,consideredasthecocycleconditionforthenaturaldoublecomplexassociatedwiththedeformationsofsuperKricheverdata.Ourapproachisbasedontheconstructionoftheuniversal
3、superdivisor(ofdegreeg),andalocaluniversalfamilyofgeometricdatawhichgivethemapintotheSuperGrassmannian.1IntroductionInthisnotewestudythegeometricalsettingofthesuperKrichevermapinanalogyarXiv:nlin/0005062v1[nlin.SI]29May2000tothestandardnongradedcase[5].Thi
4、smapisanessentialtoolintheanalysisofthealgebraicgeometricsolutionstointegrablesystemsofsolitontype(see,e.g.,[10]).Itssuperextensionhasalreadybeenintroducedin[11],andstudiedin[12,1].Theessentialdifferenceinourapproachistomakefullprofitoftheso–calledFa`adiBrun
5、oapproachtotheKPtheory[4]anditssupergeneralization[6],wheretheequivalenceofthisapproachtothestandarddifferential-operatorapproachtotheJacobianSKP[9,12]isproved.Itturnsout,asintheclassicalcase,thattheFa`adiBrunorecursionrelationis(relatedto)thefirstcocyclecon
6、ditionforthehypercohomologygroupwhichcontrolstheinfinitesimaldeformationsofthespectralsuperlinebundletogetherwithitsmeromorphicsections.Thebasicadvantageofthisapproachisthatitisdirectlyrelatedtothe(Su-per)Grassmanniandescriptionofthehierarchy,andhasanintrin
7、sicgeometricalmean-ing.Inparticular,wecanavoidthedifficultinitialstepoftheintroductionofthe1Baker–Akhiezerfunction,goonwiththenaturaldevelopmentofthegeometricalcon-struction,andrecovertheexistenceoftheBAfunctionattheend.Asintheclassicalcase,theimportanttechn
8、icaltoolistoconstructalocaluniver-saldeformationoftheinitialsuperlinebundle,sincethecocycleconditioncomesbyconsideringpoint-wisethegermofsuchadeformationasavectorfieldonthebase.Thisisadifficultpointbecausewelack
