  The Hartshorne conjecture predicts that two submanifolds X and Y in a
projective manifold Z with ample normal bundles meets as soon as dim X + dim Y
is at least dim Z. We mostly assume slightly stronger that one of the normal
bundles is positive in the sense of Griffiths. We observe that the conjecture
holds generically, relate it to question on cones of cycles and verify it in
various cases.
