▁the ▁sequence ▁of ▁sub she aves ▁ ▁if ▁ ▁is ▁invert ible ▁ ▁where ▁ ▁is ▁the ▁higher ▁adj unction ▁ideal . ▁Problem . ▁Is ▁ ▁finit ely ▁generated ? ▁If ▁this ▁is ▁true ▁then ▁ ▁is ▁called ▁the ▁relative ▁canonical ▁model ▁of ▁, ▁or ▁the ▁canonical ▁blow - up ▁of ▁. ▁ ▁Some ▁basic ▁properties ▁were ▁as ▁follows : ▁The ▁relative ▁canonical ▁model ▁was ▁independent ▁of ▁the ▁choice ▁of ▁resolution . ▁ ▁Some ▁ ▁integer ▁multiple ▁ ▁of ▁the ▁canonical ▁divis or ▁of ▁the ▁relative ▁canonical ▁model ▁was ▁Cart ier ▁and ▁the ▁number ▁of ▁exception al ▁components ▁where ▁this ▁agre es ▁with ▁the ▁same ▁multiple ▁of ▁the ▁canonical ▁divis or ▁of ▁Y ▁is ▁also ▁independent ▁of ▁the ▁choice ▁of ▁Y . ▁When ▁it ▁equals ▁the ▁number ▁of ▁components ▁of ▁Y ▁it ▁was ▁called ▁cre p ant . ▁It ▁was ▁not ▁known ▁whether ▁relative ▁canonical ▁models ▁were ▁C ohen – M aca ul ay . ▁ ▁Because ▁the ▁relative ▁canonical ▁model ▁is ▁independent ▁of ▁, ▁most ▁authors ▁simplify ▁the ▁termin ology , ▁ ▁referring ▁to ▁it ▁as ▁the ▁relative ▁canonical ▁model ▁of ▁▁ ▁rather ▁than ▁either ▁the ▁relative ▁canonical ▁model ▁of ▁▁ ▁or ▁the ▁canonical ▁blow - up ▁of ▁. ▁The ▁class ▁of ▁vari eties ▁that ▁are ▁relative ▁canonical ▁models ▁have ▁canonical ▁singular ities . ▁Since ▁that ▁time ▁in ▁the ▁ 1 9 7 0 s ▁other ▁mathemat icians ▁solved ▁aff irm atively ▁the ▁problem ▁of ▁whether ▁they ▁are ▁C ohen – M aca ul ay . ▁The ▁minimal ▁model ▁program ▁started ▁by