代数几何方法.第2卷（英文）
- 作者
- 出版社 哈尔滨工业大学出版社
- 出版时间 2021年6月 第1版
- ISBN 9787560394282
- 定价 68.00
内容简介
ThisVolumegivesanaccountoftheprincipalmethodsusedindevelopingatheoryofalgebraicvarietiesinspaceofndimensions.Applicationsofthesemethodsarealsogiventosomeofthemoreimportantvarietieswhichoccurinprojectivegeometry.Itwasorigina113ourintentiontoincludeanaccountofthearithmetictheoryofvarieties，andofthefoundationsofbirationalgeometry，butithasturnedouttobemoreconvenienttoreservethesetopicsforathirdvolume.Thetheoryofalgebraicvarietiesdevelopedinthisvolumeisthereforemainlyatheoryofvarietiesinprojectivespace.Inwritingthisvolumewehavebeenfacedwithtwoproblems：thedifficultquestionofwhatmustgoinandwhatshouldbeleftout，andtheproblemofthedegreeofgeneralitytobeaimedat.Asourobjectivehasbeentogiveanaccountofthemodernalgebraicmethodsavailabletogeometers，wehavenotsoughtgeneralityforitsownsake.Thereisstillenoughtobedoneintherealmofclassicalgeometrytogivethesemethodsallthescopethatcouldbedesired，andhaditbeenpossibletoconfineourselvestotheclassicalcaseofgeometryoverthefieldofcomplexnumbers，weshouldhavebeencontenttodoso.Butinordertoputtheclassicalmethodsonasoundbasis，usingalgebraicmethods，itisnecessarytoconsidergeometryovermoregeneralfieldsthanthefieldofcomplexnumbers.However，iftheultimateobjectistoprovideasoundalgebraicbasisforclassicalgeometry，itisonlynecessarytoconsiderfieldswithoutcharacteristic.Sincegeometryoveranyfieldwithoutcharacteristicconformstothegeneralpatternofgeometryoverthefieldofcomplexnumbers，wehavedevelopedthetheoryofalgebraicvarietiesoveranyfieldwithoutcharacteristic.Thusfieldswithfinitecharacteristicarenotusedinthisbook.
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