▁k - vector ▁space ▁of ▁global ▁sections ▁H 0 ( X , ▁O ( D )) ▁can ▁be ▁identified ▁with ▁the ▁set ▁of ▁effective ▁divis ors ▁linear ly ▁equivalent ▁to ▁D , ▁called ▁the ▁complete ▁linear ▁system ▁of ▁D . ▁A ▁project ive ▁linear ▁sub space ▁of ▁this ▁project ive ▁space ▁is ▁called ▁a ▁linear ▁system ▁of ▁divis ors . ▁ ▁One ▁reason ▁to ▁study ▁the ▁space ▁of ▁global ▁sections ▁of ▁a ▁line ▁bundle ▁is ▁to ▁understand ▁the ▁possible ▁maps ▁from ▁a ▁given ▁variety ▁to ▁project ive ▁space . ▁This ▁is ▁essential ▁for ▁the ▁classification ▁of ▁algebraic ▁vari eties . ▁Exp licit ly , ▁a ▁morph ism ▁from ▁a ▁variety ▁X ▁to ▁project ive ▁space ▁P n ▁over ▁a ▁field ▁k ▁determ ines ▁a ▁line ▁bundle ▁L ▁on ▁X , ▁the ▁pull back ▁of ▁the ▁standard ▁line ▁bundle ▁O ( 1 ) ▁on ▁P n . ▁Moreover , ▁L ▁comes ▁with ▁n + 1 ▁sections ▁whose ▁base ▁loc us ▁( the ▁intersection ▁of ▁their ▁zero ▁sets ) ▁is ▁empty . ▁Con vers ely , ▁any ▁line ▁bundle ▁L ▁with ▁n + 1 ▁global ▁sections ▁whose ▁common ▁base ▁loc us ▁is ▁empty ▁determ ines ▁a ▁morph ism ▁X ▁→ ▁P n . ▁These ▁observations ▁lead ▁to ▁several ▁not ions ▁of ▁posit ivity ▁for ▁Cart ier ▁divis ors ▁( or ▁line ▁bund les ), ▁such ▁as ▁am ple ▁divis ors ▁and ▁ne f ▁divis ors . ▁ ▁For ▁a ▁divis or ▁D ▁on ▁a ▁project ive ▁variety ▁X ▁over ▁a ▁field ▁k , ▁the ▁k