Abstract
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 and p ≤ n. Finally, using our characterization, we give a (partial) answer to a question posed recently by Franco, Kleiman and Lascu ([5]) on self-linking and complete intersections in positive characteristic.
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