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1、SpringerMonographsinMathematicsForfurthervolumespublishedinthisseries,www.springer.com/series/3733JohannesJ.DuistermaatDiscreteIntegrableSystemsQRTMapsandEllipticSurfacesJohannesJ.Duistermaat(deceased,March2010)ISSN1439-7382ISBN978-1-4419-7116-6e-ISBN978-0-387-7
2、2923-7DOI10.1007/978-0-387-72923-7SpringerNewYorkDordrechtHeidelbergLondonLibraryofCongressControlNumber:2010934229©SpringerScience+BusinessMedia,LLC2010Allrightsreserved.Thisworkmaynotbetranslatedorcopiedinwholeorinpartwithoutthewrittenpermissionofthepublisher(
3、SpringerScience+BusinessMedia,LLC,233SpringStreet,NewYork,NY10013,USA),exceptforbriefexcerptsinconnectionwithreviewsorscholarlyanalysis.Useinconnectionwithanyformofinformationstorageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilarmethod
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5、rSpringerispartofSpringerScience+BusinessMedia(www.springer.com)ContentsPreface............................................................vii1TheQRTMap.................................................11.1TheRationalFormulafortheQRTMap........................11.
6、2IndeterminacyoftheQRTMap...............................31.3Reconstruction.............................................42ThePencilofBiquadraticCurvesinP1×P1......................92.1ComplexAnalyticGeometry.................................102.2ComplexProjectiveVa
7、rieties.................................282.3EllipticCurves.............................................332.4BiquadraticCurves.........................................492.5TheQRTMappingonaSmoothBiquadraticCurve..............602.6RealPoints.......................
8、.........................743TheQRTsurface...............................................853.1ThesurfaceinP1×(P1×P1)................................863.2BlowingUp.....
