7 stories in blow up.pdf

《7 stories in blow up.pdf》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、thProceedingsof12G¨okovaPublishedonlineatGeometry-TopologyConferenceGokovaGT.orgpp.1–48SevenshortstoriesonblowupsandresolutionsHerwigHauserToRaoulBott–withgreatrespect.“Atthattime,blowupswerethepoorman’stooltoresolvesingularities.”Thisphraseofthelate21stcenturymathematicianJ.H.Φ.Leichtcouldbec

2、omecorrect.Inourdays,however,blowupsarestillthemaindeviceforresolutionpurposes(cf.fig.1).Figure1:ResolutionofthesurfaceHelix:x2−x4=y2z2bytwoblowups.Thesenotesshallgiveaninformalintroductiontothesubject.Theyarecomplementedbythediscussionofmanyspecialandlessknownfeaturesofblowups.Thelecturesadres

3、stostudentsandgeometerswhoarenotexpertsinthefield,butwhoneedtouseblowupsoccasionallyorwhojustwanttohaveagoodcomprehensionofthem.Referencesarescatteredintheliteratureandmostlyconcentrateononlypartofthestory.Thistextisneithercomplete,buthintsatleastatthevarietyofproperties,resultsandtechniqueswhi

4、charerelatedtoblowupsandwhichmakethemsoattractive.Actually,itmayserveasthestartingpointtowriteacomprehensivetreatiseonblowups(whichshouldinparticularincludethesolutionstoallexercises).Theobviousobjectionfromalgebraicgeometerstosuchaprojectwillbethatblowupsaretoosimpletodeserveaseparatetreatmen

5、t.Themanyopenandintricatequestionslistedinthesenotesmayserveasareplytothisreproach.ThematerialstemsfromlecturesheldbytheauthorattheMathematicalSciencesRe-searchInstitute(MSRI)atBerkeleyinAprilandMay2004andduringtheConferenceonGeometryandTopologyatG¨okova,Turkey,inJune2005.Bothclassesweretaught

6、SupportedinpartbyFWF-projectP15551,andthebilateralexchangeprogramAccionesIntegradas.1H.Hauserextemporeinordertoreactbettertothedoubtsandquestionsoftheaudience.Andthenicestcomplimentwastheremarkofasolidalgebraicgeometersaying“Ithoughttoknowalreadyallaboutblowups,butIamnolongersureaboutthis”.Wea

7、reverygratefultoFrankSottileandSelmanAkbulutforthekindinvitationstoBerkeleyandG¨okova,andtoallthepeoplefromMSRIfortheirwarmhospitality.Thestudentsoftheclassesinterferedmanytimeswithinterestingremarksandinquiries–thishelpedalottoshapethe