On a special class of smooth codimension two subvarieties in Pn, n⩾5☆

Abstract We consider smooth codimension two subcanonical subvarieties in P n with n ⩾ 5 , lying on a hypersurface of degree s having a linear subspace of multiplicity s - 2 . We prove that such varieties are complete intersections. We also give a little improvement to some earlier results on the non existence of rank two vector bundles on P 4 with small Chern classes.