▁on ▁project ive ▁space . ▁ ▁Gro th end ieck ▁generalized ▁Le f sch etz ' s ▁theorem ▁in ▁several ▁directions , ▁involving ▁arbitrary ▁base ▁fields , ▁singular ▁vari eties , ▁and ▁results ▁on ▁local ▁rings ▁rather ▁than ▁project ive ▁vari eties . ▁In ▁particular , ▁if ▁R ▁is ▁a ▁complete ▁intersection ▁local ▁ring ▁which ▁is ▁factor ial ▁in ▁cod im ension ▁at ▁most ▁ 3 ▁( for ▁example , ▁if ▁the ▁non - regular ▁loc us ▁of ▁R ▁has ▁cod im ension ▁at ▁least ▁ 4 ), ▁then ▁R ▁is ▁a ▁unique ▁factor ization ▁domain ▁( and ▁hence ▁every ▁We il ▁divis or ▁on ▁Spec ( R ) ▁is ▁Cart ier ). ▁The ▁dimension ▁bound ▁here ▁is ▁optimal , ▁as ▁shown ▁by ▁the ▁example ▁of ▁the ▁ 3 - dimensional ▁quad ric ▁cone , ▁above . ▁ ▁Notes ▁ ▁References ▁▁▁▁ ▁Section ▁II . 6 ▁of ▁ ▁External ▁links ▁ ▁Category : Ge ometry ▁of ▁divis ors <0x0A> </s> ▁D itt mer ▁may ▁refer ▁to : ▁ ▁People ▁Andreas ▁D itt mer ▁( born ▁ 1 9 7 2 ), ▁German ▁s print ▁can oe ist ▁An ja ▁D itt mer ▁( born ▁ 1 9 7 5 ), ▁German ▁tri ath lete ▁Er ica ▁D itt mer ▁( born ▁ 1 9 9 1 ), ▁American - born ▁Mexican ▁sw immer ▁Felix ▁D itt mer ▁( 1 9 0 4 – 1 9 7 7 ), ▁Australian ▁politician ▁Jack ▁D itt mer ▁( 1 9 2 8 – 2 0 1