  Developing a previous idea of Faltings, we characterize the complete
intersections of codimension 2 in P^n, n>=3, over an algebraically closed field
of any characteristic, among l.c.i. X, as those that are subcanonical and
scheme-theoretically defined by p<=n-1 equations. Moreover, we give some other
results assuming that the normal bundle of X extends to a numerically split
bundle on P^n, p<=n and the characteristic of the base field is zero. Finally,
we give a (partial) answer to a question posed recently by Franco, Kleiman and
Lascu on self-linking and complete intersections in positive characteristic.
