资源描述：
《moduli of curves - j. harris, i. morrison》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,techniqu
2、esandviewpointsintroducedbyMumfordandothers,havemadeitpossibleforustounderstandthebehaviorofcurvesinwaysthatsimplywerenotpossi-bleahalf-centuryago.Thisinturnhasled,overthelastfewdecades,toaburstofactivityinthearea,resolvinglong-standingproblemsandgeneratingnewandunforeseenresultsandquestions.Wehopet
3、oacquaintyoubothwiththeseresultsandwiththeideasthathavemadethempossible.Thebookisn’tintendedtobeadefinitivereference:thesubjectisdevelopingtoorapidlyforthattobeafeasiblegoal,evenifwehadtheexpertisenecessaryforthetask.Ourpreferencehasbeentofo-cusonexamplesandapplicationsratherthanonfoundations.Whendis
4、cussingtechniqueswe’vechosentosacrificeproofsofsome,evenbasic,results—particularlywherewecanprovideagoodreference—inordertoshowhowthemethodsareusedtostudymoduliofcurves.Likewise,weoftenproveresultsinspecialcaseswhichwefeelbringouttheimportantideaswithaminimumoftechnicalcomplication.Chapters1and2provi
5、deasynopsisofbasictheoremsandconjec-turesaboutHilbertschemesandmodulispacesofcurves,withfewornodetailsabouttechniquesorproofs.Usethemmoreasaguidetotheliteraturethanasaworkingmanual.Chapters3through6are,bycontrast,considerablymoreself-containedandapproachable.Ul-timately,ifyouwanttoinvestigatefullyan
6、yofthetopicswediscuss,you’llhavetogobeyondthematerialhere;butyouwilllearnthetech-niquesfullyenough,andseeenoughcompleteproofs,thatwhenyoufinishasectionhereyou’llbeequippedtogoexploringonyourown.Ifyourgoalistoworkwithfamiliesofcurves,we’dthereforesuggestthatyoubeginbyskimmingthefirsttwochaptersandthent
7、acklethelaterchaptersindetail,referringbacktothefirsttwoasnecessary.viiiContentsAsforthecontentsofthebook:Chapters1and2arelargelyexposi-tory:forthemostpart,wediscussingeneraltermstheproblemsas-sociated
