▁ ▁The ▁We il ▁divis or ▁class ▁group ▁Cl ( X ) ▁is ▁the ▁quot ient ▁of ▁Div ( X ) ▁by ▁the ▁subgroup ▁of ▁all ▁principal ▁We il ▁divis ors . ▁Two ▁divis ors ▁are ▁said ▁to ▁be ▁linear ly ▁equivalent ▁if ▁their ▁difference ▁is ▁principal , ▁so ▁the ▁divis or ▁class ▁group ▁is ▁the ▁group ▁of ▁divis ors ▁mod ulo ▁linear ▁equivalence . ▁For ▁a ▁variety ▁X ▁of ▁dimension ▁n ▁over ▁a ▁field , ▁the ▁divis or ▁class ▁group ▁is ▁a ▁Ch ow ▁group ; ▁namely , ▁Cl ( X ) ▁is ▁the ▁Ch ow ▁group ▁CH n − 1 ( X ) ▁of ▁( n − 1 )- dimensional ▁cycles . ▁ ▁Let ▁Z ▁be ▁a ▁closed ▁subset ▁of ▁X . ▁If ▁Z ▁is ▁ir reducible ▁of ▁cod im ension ▁one , ▁then ▁Cl ( X ▁− ▁Z ) ▁is ▁is omorphic ▁to ▁the ▁quot ient ▁group ▁of ▁Cl ( X ) ▁by ▁the ▁class ▁of ▁Z . ▁If ▁Z ▁has ▁cod im ension ▁at ▁least ▁ 2 ▁in ▁X , ▁then ▁the ▁restriction ▁Cl ( X ) ▁→ ▁Cl ( X ▁− ▁Z ) ▁is ▁an ▁isomorphism . ▁( Th ese ▁facts ▁are ▁special ▁cases ▁of ▁the ▁local ization ▁sequence ▁for ▁Ch ow ▁groups .) ▁ ▁On ▁a ▁normal ▁integral ▁No ether ian ▁scheme ▁X , ▁two ▁We il ▁divis ors ▁D , ▁E ▁are ▁linear ly ▁equivalent ▁if ▁and ▁only ▁if ▁ ▁and ▁ ▁are ▁is omorphic ▁as ▁- modules . ▁Is omorphism ▁classes ▁of ▁ref lex ive