eisenbud d. the geometry of syzygies (draft 2004, springer, gtm 229, 2005)( 0387222324)(241s)mag外语英文电子书

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1、ThisispagevPrinter:OpaquethisContentsPreface:AlgebraandGeometryixWhatAreSyzygies?...................................ixTheGeometricContentofSyzygies..........................xiWhatDoesSolvingLinearEquationsMean?.....................xiExperimentandComp

2、utation.............................xiiWhat'sInThisBook?..................................xiiiPrerequisites.......................................xvHowDidThisBookComeAbout?...........................xvOtherBooks.......................................

3、xvThanks..........................................xvNotation.........................................xvi1FreeResolutionsandHilbertFunctions1TheGenerationofInvariants..............................1EnterHilbert.......................................21A

4、TheStudyofSyzygies..................................2TheHilbertFunctionBecomesPolynomial......................41BMinimalFreeResolutions................................5DescribingResolutions:BettiDiagrams........................7PropertiesoftheGradedB

5、ettiNumbers.......................8TheInformationintheHilbertFunction.......................91CExercises.........................................92FirstExamplesofFreeResolutions132AMonomialIdealsandSimplicialComplexes......................13Simplicia

6、lComplexes..................................13LabelingbyMonomials.................................14SyzygiesofMonomialIdeals..............................16viContents2BBoundsonBettiNumbersandProofofHilbert'sSyzygyTheorem.........1832CGeometryfromSyzy

7、gies:SevenPointsinP.....................20TheHilbertPolynomialandFunction..........................20...andOtherInformationintheResolution......................222DExercises.........................................2423PointsinP293ATheIdealofaFiniteSe

8、tofPoints...........................303BExamples.........................................373CExistenceofSetsofPointswithGivenInvariants...................403DExercises.........................................444Castelnuovo{MumfordRegularity514ADenit