classical algebraic geometry_a morden view_1107017653algebgeometry

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1、ClassicalAlgebraicGeometry:amodernviewIGORV.DOLGACHEVPrefaceThemainpurposeofthepresenttreatiseistogiveanaccountofsomeofthetopicsinalgebraicgeometrywhichwhilehavingoccupiedthemindsofmanymathematiciansinpreviousgenerationshavefallenoutoffashioninmoderntimes.Oftenint

2、hehistoryofmathematicsnewideasandtechniquesmaketheworkofpreviousgenerationsofresearchersobsolete,especiallythisappliestothefoundationsofthesubjectandthefundamentalgeneraltheoreticalfactsusedheavilyinresearch.Eventhegreatestachievementsofthepastgenera-tionswhichcan

3、befoundforexampleintheworkofF.SeverionalgebraiccyclesorintheworkofO.Zariski’sinthetheoryofalgebraicsurfaceshavebeengreatlygeneralizedandclarifiedsothattheynowremainonlyofhistor-icalinterest.Incontrast,thefactthatanonsingularcubicsurfacehas27linesorthataplanequartic

4、has28bitangentsissomethingthatcannotbeimproveduponandcontinuestofascinatemoderngeometers.Oneofthegoalsofthispresentworkisthentosavefromobliviontheworkofmanymathematicianswhodiscoveredtheseclassictenetsandmanyotherbeautifulresults.Inwritingthisbookthegreatestchalle

5、ngetheauthorhasfacedwasdistillingthematerialdowntowhatshouldbecovered.Thenumberofconcretefacts,examplesofspecialvarietiesandbeautifulgeometricconstructionsthathaveaccumulatedduringtheclassicalperiodofdevelopmentofalgebraicgeometryisenormousandwhatthereaderisgoingt

6、ofindinthebookisreallyonlyatipoftheiceberg;aworkthatissortofatastesamplerofclassicalalgebraicgeometry.Itavoidsmostofthematerialfoundinothermodernbooksonthesubject,suchas,forexample,[10]whereonecanfindmanyoftheclassicalresultsonalgebraiccurves.Instead,ittriestoassemb

7、leor,inotherwords,tocreateacompendiumofmaterialthateithercannotbefound,istoodispersedtobefoundeasily,orissimplynottreatedadequatelybycontemporaryresearchpapers.Ontheotherhand,whilemostofthematerialtreatedinthebookexistsinclassicaltreatisesinalgebraicgeometry,their

8、somewhatarchaicterminologyivPrefaceandwhatisbynowcompletelyforgottenbackgroundknowledgemakesthesebooksusefultobutahandfulofexpertsintheclassicalliteratu