资源描述:
《gtm187.moduli.of.curves,.harris,.morrison.(曲线模)》由会员上传分享,免费在线阅读,更多相关内容在学术论文-天天文库。
1、ModuliofCurvesJoeHarrisIanMorrisonSpringerToPhilGriffithsandDavidMumfordPrefaceAimsTheaimofthisbookistoprovideaguidetoarichandfascinatingsub-ject:algebraiccurves,andhowtheyvaryinfamilies.Therevolutionthatthefieldofalgebraicgeometryhasundergonewiththeintroduc-tionofschemes,togetherwithnewideas,t
2、echniquesandviewpointsintroducedbyMumfordandothers,havemadeitpossibleforustounderstandthebehaviorofcurvesinwaysthatsimplywerenotpossi-bleahalf-centuryago.Thisinturnhasled,overthelastfewdecades,toaburstofactivityinthearea,resolvinglong-standingproblemsandgeneratingnewandunforeseenresultsandque
3、stions.Wehopetoacquaintyoubothwiththeseresultsandwiththeideasthathavemadethempossible.Thebookisn’tintendedtobeadefinitivereference:thesubjectisdevelopingtoorapidlyforthattobeafeasiblegoal,evenifwehadtheexpertisenecessaryforthetask.Ourpreferencehasbeentofo-cusonexamplesandapplicationsratherthan
4、onfoundations.Whendiscussingtechniqueswe’vechosentosacrificeproofsofsome,evenbasic,results—particularlywherewecanprovideagoodreference—inordertoshowhowthemethodsareusedtostudymoduliofcurves.Likewise,weoftenproveresultsinspecialcaseswhichwefeelbringouttheimportantideaswithaminimumoftechnicalcom
5、plication.Chapters1and2provideasynopsisofbasictheoremsandconjec-turesaboutHilbertschemesandmodulispacesofcurves,withfewornodetailsabouttechniquesorproofs.Usethemmoreasaguidetotheliteraturethanasaworkingmanual.Chapters3through6are,bycontrast,considerablymoreself-containedandapproachable.Ul-tim
6、ately,ifyouwanttoinvestigatefullyanyofthetopicswediscuss,you’llhavetogobeyondthematerialhere;butyouwilllearnthetech-niquesfullyenough,andseeenoughcompleteproofs,thatwhenyoufinishasectionhereyou’llbeequippedtogoexploringonyourown.Ifyourgoalistoworkwithfamiliesofcurves,we’dthereforesuggestthatyo
7、ubeginbyskimmingthefirsttwochaptersandthentacklethelaterchaptersindetail,referringbacktothefirsttwoasnecessary.viiiContentsAsforthecontentsofthebook:Chapters1and2arelargelyexposi-tory:forthemostpart,wediscussingeneraltermstheproblemsas-sociated