▁Camp ana ▁and ▁K oll ár – M i ya oka – M ori ▁showed ▁that ▁a ▁smooth ▁F ano ▁variety ▁over ▁an ▁algebra ically ▁closed ▁field ▁is ▁r ation ally ▁chain ▁connected ; ▁that ▁is , ▁any ▁two ▁closed ▁points ▁can ▁be ▁connected ▁by ▁a ▁chain ▁of ▁rational ▁curves . ▁K oll ár – M i ya oka – M ori ▁also ▁showed ▁that ▁the ▁smooth ▁F ano ▁vari eties ▁of ▁a ▁given ▁dimension ▁over ▁an ▁algebra ically ▁closed ▁field ▁of ▁characteristic ▁zero ▁form ▁a ▁bounded ▁family , ▁meaning ▁that ▁they ▁are ▁class ified ▁by ▁the ▁points ▁of ▁finit ely ▁many ▁algebraic ▁vari eties . ▁In ▁particular , ▁there ▁are ▁only ▁finit ely ▁many ▁de formation ▁classes ▁of ▁F ano ▁vari eties ▁of ▁each ▁dimension . ▁In ▁this ▁sense , ▁F ano ▁vari eties ▁are ▁much ▁more ▁special ▁than ▁other ▁classes ▁of ▁vari eties ▁such ▁as ▁vari eties ▁of ▁general ▁type . ▁ ▁Classification ▁in ▁small ▁dimensions ▁ ▁The ▁following ▁discussion ▁concerns ▁smooth ▁F ano ▁vari eties ▁over ▁the ▁complex ▁numbers . ▁ ▁A ▁F ano ▁curve ▁is ▁is omorphic ▁to ▁the ▁project ive ▁line . ▁ ▁A ▁F ano ▁surface ▁is ▁also ▁called ▁a ▁del ▁Pe z zo ▁surface . ▁Every ▁del ▁Pe z zo ▁surface ▁is ▁is omorphic ▁to ▁either ▁P 1 ▁× ▁P 1 ▁or ▁to ▁the ▁project ive ▁plane ▁blow n ▁up ▁in ▁at ▁most ▁ 8 ▁points , ▁which ▁must ▁be ▁in ▁general ▁position . ▁As ▁a ▁result , ▁they ▁are ▁all ▁rational . ▁ ▁In ▁dimension