Feynman motives of banana graphs(16)

OneproceduretodealwiththissourceofdivergencesistoworkonblowupsofPn 1alongthissingularlocus(cf.[11],[10]).In[26]anotherpossiblemethodofregularizationforintegralsoftheform(1.33)whichtakescareofthesingularitiesoftheintegralonσn(thepoleoftheGammafunctionneedstobeaddressedseparately)wasproposed,basedonreplacingtheintegralalongσnwithanintegralthatgoesaroundthesingularitiesalongthe bersofacirclebundle.Ingeneral,thistypeofregularizationproceduresrequiresadetailedknowledgeofthesingularitiesofthehypersurfaceXΓtobecarriedout,andthatisoneofthereasonsforintroducinginvariantsofsingularvarietiesinthestudyofgraphhypersurfaces. withthefunctionoftheexternalmomentagivenbyC(p)=(Pv)2,withvbeingeither oneofthetwoverticesofthegraphΓnandPv=e∈Eext(Γn),t(e)=vpe.

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