▁form ). ▁ ▁Let ▁D ▁be ▁a ▁smooth ▁cod im ension - 1 ▁sub vari ety ▁in ▁P n . ▁The ▁adj unction ▁formula ▁implies ▁that ▁K D ▁= ▁( K X ▁+ ▁D )| D ▁= ▁( − ( n + 1 ) H ▁+ ▁deg ( D ) H )| D , ▁where ▁H ▁is ▁the ▁class ▁of ▁a ▁hyper plane . ▁The ▁hyp ers ur face ▁D ▁is ▁therefore ▁F ano ▁if ▁and ▁only ▁if ▁deg ( D ) ▁< ▁n + 1 . ▁ ▁More ▁generally , ▁a ▁smooth ▁complete ▁intersection ▁of ▁hyp ers ur faces ▁in ▁n - dimensional ▁project ive ▁space ▁is ▁F ano ▁if ▁and ▁only ▁if ▁the ▁sum ▁of ▁their ▁degrees ▁is ▁at ▁most ▁n . ▁ ▁We ight ed ▁project ive ▁space ▁P ( a 0 ,..., an ) ▁is ▁a ▁singular ▁( k lt ) ▁F ano ▁variety . ▁This ▁is ▁the ▁project ive ▁scheme ▁associated ▁to ▁a ▁grad ed ▁polynomial ▁ring ▁whose ▁gener ators ▁have ▁degrees ▁a 0 ,..., an . ▁If ▁this ▁is ▁well ▁formed , ▁in ▁the ▁sense ▁that ▁no ▁n ▁of ▁the ▁numbers ▁a ▁have ▁a ▁common ▁factor ▁greater ▁than ▁ 1 , ▁then ▁any ▁complete ▁intersection ▁of ▁hyp ers ur faces ▁such ▁that ▁the ▁sum ▁of ▁their ▁degrees ▁is ▁less ▁than ▁a 0 + ... + an ▁is ▁a ▁F ano ▁variety . ▁ ▁Every ▁project ive ▁variety ▁in ▁characteristic ▁zero ▁that ▁is ▁hom ogeneous ▁under ▁a ▁linear ▁algebraic ▁group ▁is ▁F ano . ▁ ▁Some ▁properties ▁