On two simple criteria for recognizing complete intersections in codimension 2

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, 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.